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if tan

~~o~~+sin~~o~~= m,tan~~o~~-sin~~o~~=n,prove that m^{2}-n^{2}=4root mnif the pair of equations x + y = root 2. and x sin A + y cos A = 1 has infinitely many solutions, then A = ?

options : 30, 45, 60 and 90

How to make working model on trigonometry?

prove that secθ + tanθ / secθ - tanθ = (1 + sinθ / cosθ)^2

if cos theta + sin theta =root2 cos theta prove that cos theta - sin theta =root 2 sin theta

sin 25/cos 65+cosec 34/sec 56-2*cos 43*cosec47/tan 10*tan 40*tan 50*tan 80

If a sin theta + b cos theta = c , then prove that a cos theta - b sin theta = the whole under root a

^{2}+ b^{2}- c^{2}.plz answer soon if u want a thumbzzzz up guys !!!!!!!!!!!!!

prove that

1+cos

~~0~~- sin^{2}~~0~~/sin~~0~~(1+cos~~0~~) = cot~~0~~if secA =x+ (1/4x), prove that secA + tanA =2x or 1/2x

rply fst!!!

if tan theta +sin theta=m, tan theta -sin theta=n show that m square -n square=4 root mn

If sec2A=cosec(A-27) where 2A is an acute angle,then the measure of

prove that tan theta/1-cot theta +cot theta/1-tan theta=1+tan theta+cot theta

Plzz answer fast

sin=theta+ costheta5/4, then find the value ofsin^{6}theta+ cos^{6}theta+7.sin^{2}theta.cos^{2}theta.If sec(theta)=x+1/4x, prove that sec(theta)+tan(theta)=2x or 1/2x

please answer my ques. Thanks in advance.

If (1 + cos) / (1 - cos) = 16/9, then find (1 + cot) / (1 - cot) ?if a+b=90. prove that root of tana.tanb + tana.cotb / sina .secb - root of sin

^{2}b / cos^{2}a=tanaProve that sin theta-cos theta+1/sin theta+cos theta-1 = 1/sec theta -tan theta.

^{2}A is?find the value of sin30 geometrically

if sec theta+tan theta =p ,prove that sin theta = (p square- 1) / (p square + 1)

tanA + secA -1 / tanA - secA + 1=1+sinA / cosA

Ques --a cot theta +b cosec theta = p, b cot theta + a cosec theta = q then find p2 - q2

Solution --theta be x

a cot x + b cosec x = p

p

^{2}.=a

^{2 }cot^{2 }x + b^{2}cosec^{2x}+2.acotx.bcosecxq

^{2}=b

^{2}cot^{2}x + a^{2 }cosec^{2}x+2.b.cotx.acosecxp2-q2=

a

^{2 }cot^{2 }x + b^{2}cosec^{2}+2.acotx.bcosecx-b

^{2}cot^{2}x - a^{2 }cosec^{2}x - 2.b.cotx.acosecx=a

^{2 }cot^{2 }x + b^{2}cosec^{2}-b^{2}cot^{2}x - a^{2 }cosec^{2}x=a

^{2 (}cot^{2 }x-^{ }cosec^{2}x ) + b^{2 (}cosec^{ 2 }x-cot^{2}x )=a

^{2}(-1) + b^{2 }(1)= b

^{2 }- a^{2in the above solution where does }a

^{2 }cot^{2 }x + b^{2}cosec^{2}+2.acotx.bcosecx-b

^{2}cot^{2}x - a^{2 }cosec^{2}x - 2.b.cotx.acosecx where does the expression formed from 2ab goes ??if A,B,c are interior angles of triangle ABC then show that sin (B+C/2) = cos A/2

Find the value of sin60 geometrically

^{0}.cos 75^{0}+cos 15^{0}.sin 75^{0}/tan 5^{0}.tan 30^{0}.tan 35^{0}.tan 55^{0}.tan 85^{0}^{2}A = 1+cot^{2}AIf acosx-bsinx =c, prove that asinx + bcosx = +- root(a

^{2}+b^{2}-c^{2})Q.prove that: sin square 6 degree+sin square 12 degree+sin square 18 degree +................sin square 84 degree+sin square 90 degree =8.

find the value of sin 30 and sin 60 , geometrically .

de value of cos1 cos2 cos 3 ....cos 180 is =?

plz answer!!!

cosA - sinA + 1 / cosA + sinA - 1 = cosecA + cotA

Answer soon plzzzzz!

If x/a cos theta+y/b sin theta=1 and x/a sin theta-y/b cos theta=1, prove that x square/a square+y square/b square=2

what does

pandit badri prasad

har har bole

sona chandi tole

means in trigonometry

Dear Expert

Kindly assist to solve the following problems:

1. If Cot Theta =2, Find the values of all other Trigonometric Ratios Theta.

2. If 5 Cot Theta = 3, Evaluate 5 Sin Theta - 3 Cos Theta / 5 Sin Theta + 3 Cos Theta.

3. Evaluate Tan

^{2}60 + 4 Cos^{2}45 + 8 Cosec^{2}60 / 2 Cosec 30 +3 Sec 60 + 7/3 Cot^{2}30.4. Evaluate (Cosec

^{2}(90 - Theta) - Tan^{2}Theta/ 4(Cos^{2}48 +Cos^{2}42)) - ( 2Tan^{2}30 x Sec^{2}52 x Sin^{2}38 / Cosec^{2})5. (Sin Theta -Cos Theta + 1 / Sin Theta + Cos Theta -1)=1 / Sec Theta - Tan Theta.

REQUESTAN URGENT REPLY, PLEASE.

if root 3 tan theta = 3 sin theta, then ( sin

^{2}thea - cos^{2 }theta) = ??prove that

(1+cot theta -cosec theta ) (1+ tan theta + sec theta) =2

evaluate: tan15 * tan25 * tan60 * tan65 * tan75 - tan30

if cosA +sinA=root2cosA show that cosA -sinA=root2 sina

Prove that

cos

^{3}A + sin^{3}A /cosA+sinA + cos^{3}A - sin^{3}A /cosA-sinA = 2an equilateral triangle is inscribed in a cirle of radius 6 cm.Find its sides

IF COT = b/a, where a ANMD b ARE REAL NO .S FIND THE VALUE OF SIN

^{2}AHere are few questions from the chapter Introduction to Trigonometry for practise:- 1. In ΔABC right angled at B, AB = 24 cm, BC = 7 m. Determine a. sin A, cos A b. sin C, cos C 2. Given 15 cot A = 8. Find sin A and sec A 3. If ∠A and ∠B are acute angles such that cos A = cos B, then show that ∠A = ∠B. 4. In ΔPQR, right angled at Q, PR + QR = 25 cm and PQ = 5 cm. Determine the values of sin P, cos P and tan P. 5. State whether the following are true or false. Justify your answer. a. The value of tan A is always less than 1.. b. cos A is the abbreviation used for the cosecant of angle A. c. cot A is the product of cot and A 6. Evaluate the following a. sin60° cos30° + sin30° cos 60° b. 2tan245° + cos230° − sin260° 7. State whether the following are true or false. Justify your answer. a. sin (A + B) = sin A + sin B b. The value of sinθ increases as θ increases c. The value of cos θ increases as θ increases d. sinθ = cos θ for all values of θ e. cot A is not defined for A = 0° 8. Show that tan 48° tan 23° tan 42° tan 67° = 1 cos 38° cos 52° − sin 38° sin 52° = 0 9. If tan 2A = cot (A− 18°), where 2A is an acute angle, find the value of A. 10. If tan A = cot B, prove that A + B = 90° 11. If sec 4A = cosec (A− 20°), where 4A is an acute angle, find the value of A. 12. Express sin 67° + cos 75° in terms of trigonometric ratios of angles between 0° and 45°. 13. Express the trigonometric ratios sin A, sec A and tan A in terms of cot A. 14. : Write all the other trigonometric ratios of ∠A in terms of sec A. 15. Prove the following identities, where the angles involved are acute angles for which the expressions are defined. 16. (sec2q -1 ) (1 - cosec2q )=…………… 17. cot2q– 1/ Sin2q = ............................ 18. Given that sinq =a/b , then cos q is equal to -------------------- 19. If sin q - cos q = 0 , then the value of (sin4q + cos4q) is ……………. 20. Eualuate(1 + cot q - cos q)(1 + tanq + sec q) 21. If x = a sec q cos Ø ; y = b sec q sin Ø and z = c tan q , then X2 / a2 + Y2 /b = ………………. 22. If cosA +cos2 A = 1, then sin2 A + sin2A= 23. Prove that sec 72/ cos ec18 + sin59/ cos31 = 2 24. If sin 2 q = √3 , find q 25. Prove that cos q - sin q =√ 2 sin q,if sin q + cos q = √2 cos q 26. Prove that (tanA+ secA- 1) / (tanA-secA + 1) = secA + tanA 27. If a cos3 q + 3 cos q sin2q = m a sin3q + 3acos2q sinq = n, 28. Prove that(m+ n)2 /3+ (m+ n)2/3= 2a 2 /3 29. If 1 secq = x + 1/4x prove that sec q + tan q = 2x or 1/2x 30. If √3 tan q = 3 sinq , evaluate sin2q - cos2q 31. Prove the following identities : 1+ sec A/SecA = sin2 A/1 - cos A 32. Prove that : 1/ secq - tanq - 1/ cosq = 1/cosq -1/ secq + tanq 33. Prove the following identity: (sin A + cosec A)2 + ( cos A + sec A )2 = 7 + tan2A + cot2A. 34. If x/a cos = y/bsin and ax/cos = by/sin = a2 –b2 prove that x2 /a2 + y2 /b2 35. If cotA =4/3 check (1 – tan2A)/ 1 + tan2A = cot2A – sin2A 36. sin (A – B) = ½, cos(A + B) = ½ find A and B 37. Evaluate tan5° tan25° tan30° tan65° tan85° 38. Verify 4(sin430° + cos 460°) – 3(cos245° – sin290°) = 2 39. Show that tan48° tan23° tan 42° tan67° = 1 40. sec4A = cosec(A – 20) find A 41. tan A = cot B prove A + B = 90 42. A, B, and C are the interior angles of DABC show that sin( B + C )/2 = cos A/2 43. In DABC, if sin (A + B – C) = √3/2 and cos(B + C – A) =1/√2, find A, B and C. 44. If cos θ = and θ + φ = 900, find the value of sin φ. 45. If tan 2A = cot ( A – 180 ), where 2A is an acute angle, find the value of A. 46. If 2sin (x/2) = 1 , then find the value of x. 47. If tan A = ½ and tan B = 1/3 , by using tan (A + B) = ( tan A + tan B )/ 1 – tan A. tan B prove that A + B = 45º 48. Express sin 76° + cos 63° in terms of trigonometric ratios of angles between 0° and 45°. 49. Prove that: 2 sec2 θ – sec4 θ – 2 cosec2 θ + cosec4 θ = cot4 θ – tan4 θ 50. Find the value of θ for which sin θ – cos θ = 0 51. Given that sin2A + cos2A = 1, prove that cot2A = cosec2A – 1 52. If sin (A + B) = 1 and sin (A – B)=1/2 0o< A + B ≤ 90o; A > B, find A and B. 53. Show that tan 620/cot 280 =1 54. If sin A + sin2A = 1, prove that cos2A + cos4A = 1. 55. If sec 4A = cosec (A – 200), where 4A is an acute angle, find the value of A. 56. Prove that (cosec θ – sec θ) (cot θ – tan θ) = (cosec θ + sec θ) (sec θ . cosec θ – 2) 57. Given that A = 60o, verify that 1 + sin A =(Cos A/2 + Sin A/2)2 58. If sin θ + cos θ = x and sin θ – cos θ = y, show that x2 + y2 = 2 59. Show that sin4θ – cos4θ = 1 – 2 cos2θ 60. If θ= 45o. Find the value of sec2θ 61. Evaluate: cos60 o cos45 o -sin60 o sin45 o 62. Find the value of tan15 o.tan25 o.tan30 o tan65 o tan85 o 63. If θ is a positive acute angle such that sec θ = cosec60o, then find the value of 2cos2 θ -1 64. Find the value of sin65-cos25 without using tables. 65. If sec5A=cosec(A-36 o). Find the value of A. 66. If 2 sin x/2 - 1 =0, find the value of x. 67. If A, B and C are interior angles of ΔABC, then prove that cos (B+C)/2 = sinA/2 68. Find the value of 9sec2A-9tan2A. 69. Prove that sin6θ+cos6θ=1-3sin2θcos2θ. 70. If 5tanθ-4=0, then find the value of (5sinθ - 4cosθ) (5sinθ + 4cosθ) 71. In ABC, <c=90o, tan A= and tan B=<3.Prove that sin A. cos B+ cos A .sin B=1. 72. In D ABC, right angled at B, if tan a =1/√3 find the value of Sin A cos C + cos A sin C. 73. Show that 2(cos4 60 + sin4 30 )- (tan2 60 + cot2 45 ) + 3sec2 30 =1/4 74. sin(50 +q ) - cos(40 -q ) + tan1 tan10 tan 20 tan 70 tan80 tan89 =1 75. Given tan A =4/3, find the other trigonometric ratios of the angle A. 76. In a right triangle ABC, right-angled at B, if tan A = 1, then verify that 2 sin A cos A = 1. 77. In D OPQ, right-angled at P, OP = 7 cm and OQ – PQ = 1 cm. Determine the values of sin Q and cos Q. 78. In D ABC, right-angled at B, AB = 24 cm, BC = 7 cm. Determine:(i) sin A , cos A(ii) sin C, cos C 79. If ÐA and ÐB are acute angles such that cos A = cos B, then show that Ð A = ÐB. 80. If cot A= 7/8 evaluate: {(1 + sinA )( 1 – sinA)} / {(1+ cosA)(1-cosA) 81. In triangle ABC, right-angled at B, if tan A = 1/√3 find the value of :(i) sin A cos C + cos A sin C (ii) Cos A cos C – sin A sin C 82. In D ABC, right angled at B, AB = 5 cm and ÐACB = 300 Determine the lengths of the sides BC and AC. 83. In D PQR, right – angled at Q, PQ = 3 cm and PR = 6 cm. Determine ÐQPR and ÐPRQ 84. If sin (A-B) = ½ ,cos(A+B ) = ½ A+ B = o < A+ B ≤ 90, A > B find A and B 85. Evaluate the following: (5cos260 + 4sec230 - tan2 45)/ (sin2 30 + cos2 30) 86. If sin 3 A = cos (A – 26), where 3 A is an acute angle, find the value of A. 87. Prove the trigonometric identities (1 - cos A)/( 1 – cos A) = (cosec A – cot A)2 88. Prove the trigonometric identities ( 1+ 1/tan2A) (1 + 1/cot2A) = 1/(sin2A- cos4A) 89. Prove the trigonometric identities (sec4A – sec2A) = tan4A +tan2A = sec 2 A tan2 A 90. Prove the trigonometric identities cotA – tanA = (2cos 2A -1)/ (sinA.cosA) 91. Prove the trigonometric identities.(1- sinA +cosA)2 = 2(1+cosA )(1 – sinA) 92. If tanA +sinA = m and tanA – sinA=n show that m2 – n2 = 4 93. If x= psecA + qtanA and y= ptan A +q secA prove that x2 – y2 = p2 – q2 94. If sinA + sin2A = 1 prove that cos2 A + cos4 A =1 95. Express the following in terms of t-ratios of angles between 0° and 45°. 1) sin 85° +cosec 85° 2) cosec 69° +cot 69° 3) sin 81° +tan 81° 4) cos 56° +cot 56° 96. [sin (90 -A) sin A]/tan A-1 = - sin² A 97. cos cos(90° - ) -sin sin (90° - ) = 0 98. sin (90° - ) cos (90° - ) = tan /(1 +tan² ) 99. cosec² (90° - ) -tan² = cos²(90° - ) +cot² 100. If cos /cos = m and cos /sin = n, show that (m² +n²) cos² = n².If x = r cos sin , y = r cos cos and z = r sin , show that x² +y² +z² = r².

if 7 sin^2

+theta^23 cos=4 .show tantheta=1/root3thetaprove sin theta-2sin cube theta/2cos cube theta-cos theta=tan theta

^{3}𝜃 + 𝑐𝑜𝑠^{3}𝜃/sin𝜃 + cos𝜃+(sin𝜃cos𝜃)=1solve (cosec theta-sin theta)(sec theta - cos theta) = 1tan theta + cot theta

If cosec theta + cot theta= p Prove that cos theta = p

^{2}-1 by p^{2}+1Given that sinθ + 2cosθ = 1, then prove that 2sinθ – cosθ = 2.

(1+ cot A - cosec A) (1+ tan A + sec A) = 2

if sin theta = c/root c2+d2 and d 0, find the value of cos theta and tan theta

cos45 degree divided by sec 30 degree plus cosec 30 degree .... hw do u solve it in simple way ... nd hw do v rationalise d denominator

If sec 4A = cosec (A - 20[degree]), where 4A is an acute angle, find the value of A.prove that tan+sec-1/tan-sec+1 =1+sin/cos

Prove that:- sin

^{6}theta + cos^{6}theta = 1-3sin^{2}theta.cos^{2}theta^{2}32 -7 cot^{2}58)If Sin + Cos = p and Sec + Cosec = q, show that q(p2 – 1) = 2p.CBSE CLASS 10 MCQ TRIGONOMETRY1. If cos A = 4/5 , then the value of tan A is(A) 3/5 (B)3/4 (C)4/3 (D)5/3

2. If sin A = 1/2 , then the value of cot A is

(A) 3 (B) 1/3 (C) 3/2 (D) 1

3. The value of the expression [cosec (75 + q) sec (15 q tan (55 + q+ cot (35 q)] is

(A) 1 (B) 0 (C) 1 (D) 3/2

4. Given that sinq= a/b , then cosq is equal to5. If cos (a + b) = 0, then sin (a - b) can be reduced to(A) cos b (B) cos 2b (C) sin α (D) sin 2a

6. The value of (tan1 tan 2 tan3 ... tan 89) is

(A) 0 (B) 1 (C) 2 (D)1 / 2

7. If cos 9a= sinα and 9a a is

(A) 1/√3 (B) √ 3 (C) 1 (D) 0

8. If DABC is right angled at C, then the value of cos (A+B) is

(A) 0 (B) 1 (C) 1/2 (D)√3/2

9. If sinA + sin

^{2}A = 1, then the value of the expression (cos^{2}A + cos^{4}A) is(A) 1 (B) 1/2 (C) 2 (D) 3

10. Given that sina= 1/2 and cosb =1/2 , then the value of (a + b) is

(A) 0 (B) 30 (C) 60 (D) 90

11. The value of the expression [sin

^{2}22^{0}sin^{2}68^{0}/ cos^{2}22^{0}cos^{2}68^{0}+ sin^{2}63^{0}cos63^{0}sin 27^{0}] is (A) 3 (B) 2 (C) 1 (D) 012. If 4 tanq = 3, then [4sinq - cosq ] / [4sinq + cos q ] is equal to

(A) 2/3 (B) 1/3 (C) 1/2 (D) 3/4

13. If sinq cosq = 0, then the value of (sin

^{4}q + cos^{4}qθ) is(A) 1 (B) 3/4 (C) 1/2 (D) 1/4

14. sin (45 + q) cos (45 q) is equal to

(A) 2cosq (B) 0 (C) 2 sin q (D) 1

15. A pole 6 m high casts a shadow 2 √3m long on theground, then the Suns elevation is

(A ) 60 (B) 45 (C) 30 (D) 90

prove that cotA + cosecA -1/ cotA - CosecA + 1 = 1 + cosA - sinA

if A and b are acute angles such that cosA=cosB, then show that ANGLEA=ANGLEB.

if 1+ sin

^{2}A = 3sinAcosA, then show that tanA =1or 1/2. plzzzzz urgen 2mrow is my examprove that

1 + sin

~~o~~/1 - sin~~o~~= (sec~~o~~+ tan~~o~~)^{2}given that sin theta + 2 cos theta = 1 , then prove that 2 sin theta -cos theta = 2

if sin 3 theta = cos ( theta-6 degree) where 3 theta and ( theta-6 degree) both r acute angle then what is the value of theta

tanA / 1-CotA + CotA / 1-TanA = 1 + TanA + Cot A

Here are few questions from the chapter Introduction to Trigonometry for practise:-1. In ΔABC right angled at B, AB = 24 cm, BC = 7 m. Determinea. sin A, cos Ab. sin C, cos C2. Given 15 cot A = 8. Find sin A and sec A3. If ∠ A and ∠ B are acute angles such that cos A = cos B, then show that ∠ A = ∠ B.4. In ΔPQR, right angled at Q, PR + QR = 25 cm and PQ = 5 cm. Determine the values of sin P, cos P and tan P.5. State whether the following are true or false. Justify your answer.a. The value of tan A is always less than 1..b. cos A is the abbreviation used for the cosecant of angle A.c. cot A is the product of cot and A6. Evaluate the followinga. sin60� cos30� + sin30� cos 60�b. 2tan245� + cos230� − sin260�7. State whether the following are true or false. Justify your answer.a. sin (A + B) = sin A + sin Bb. The value of sinθ increases as θ increasesc. The value of cos θ increases as θ increasesd. sinθ = cos θ for all values of θe. cot A is not defined for A = 0�8. Show that tan 48� tan 23� tan 42� tan 67� = 1cos 38� cos 52� − sin 38� sin 52� = 09. If tan 2A = cot (A− 18�), where 2A is an acute angle, find the value of A.10. If tan A = cot B, prove that A + B = 90�11. If sec 4A = cosec (A− 20�), where 4A is an acute angle, find the value of A.12. Express sin 67� + cos 75� in terms of trigonometric ratios of angles between 0� and 45�.13. Express the trigonometric ratios sin A, sec A and tan A in terms of cot A.14. : Write all the other trigonometric ratios of ∠ A in terms of sec A.15. Prove the following identities, where the angles involved are acute angles for which the expressions are defined.16. (sec2q -1 ) (1 - cosec2q )=……………17. cot2q– 1/ Sin2q = ............................18. Given that sinq =a/b , then cos q is equal to --------------------19. If sin q - cos q = 0 , then the value of (sin4q + cos4q) is …………….20. Eualuate(1 + cot q - cos q)(1 + tanq + sec q)21. If x = a sec q cos � ; y = b sec q sin � and z = c tan q , then X2 / a2 + Y2 /b = ……………….22. If cosA +cos2 A = 1, then sin2 A + sin2A=23. Prove that sec 72/ cos ec18 + sin59/ cos31 = 2 24. If sin 2 q = √3 , find q25. Prove that cos q - sin q =√ 2 sin q,if sin q + cos q = √2 cos q26. Prove that (tanA+ secA- 1) / (tanA-secA + 1) = secA + tanA27. If a cos3 q + 3 cos q sin2q = m a sin3q + 3acos2q sinq = n, 28. Prove that(m+ n)2 /3+ (m+ n)2/3= 2a 2 /329. If 1 secq = x + 1/4x prove that sec q + tan q = 2x or 1/2x30. If √3 tan q = 3 sinq , evaluate sin2q - cos2q31. Prove the following identities : 1+ sec A/SecA = sin2 A/1 - cos A32. Prove that : 1/ secq - tanq - 1/ cosq = 1/cosq -1/ secq + tanq33. Prove the following identity:(sin A + cosec A)2 + ( cos A + sec A )2 = 7 + tan2A + cot2A.34. If x/a cos = y/bsin and ax/cos = by/sin = a2 –b2 prove that x2 /a2 + y2 /b235. If cotA =4/3 check (1 – tan2A)/ 1 + tan2A = cot2A – sin2A36. sin (A – B) = �, cos(A + B) = � find A and B37. Evaluate tan5� tan25� tan30� tan65� tan85�38. Verify 4(sin430� + cos 460�) – 3(cos245� – sin290�) = 239. Show that tan48� tan23� tan 42� tan67� = 140. sec4A = cosec(A – 20) find A41. tan A = cot B prove A + B = 9042. A, B, and C are the interior angles of DABC show that sin( B + C )/2 = cos A/2 43. In DABC, if sin (A + B – C) = √3/2 and cos(B + C – A) =1/√2, find A, B and C.44. If cos θ = and θ + φ = 900, find the value of sin φ.45. If tan 2A = cot ( A – 180 ), where 2A is an acute angle, find the value of A.46. If 2sin (x/2) = 1 , then find the value of x. 47. If tan A = � and tan B = 1/3 , by using tan (A + B) = ( tan A + tan B )/ 1 – tan A. tan B prove that A + B = 45�48. Express sin 76� + cos 63� in terms of trigonometric ratios of angles between 0� and 45�.49. Prove that: 2 sec2 θ – sec4 θ – 2 cosec2 θ + cosec4 θ = cot4 θ – tan4 θ 50. Find the value of θ for which sin θ – cos θ = 051. Given that sin2A + cos2A = 1, prove that cot2A = cosec2A – 152. If sin (A + B) = 1 and sin (A – B)=1/2 0o< A + B ≤ 90o; A > B, find A and B.53. Show that tan 620/cot 280 =154. If sin A + sin2A = 1, prove that cos2A + cos4A = 1.55. If sec 4A = cosec (A – 200), where 4A is an acute angle, find the value of A.56. Prove that (cosec θ – sec θ) (cot θ – tan θ) = (cosec θ + sec θ) (sec θ . cosec θ – 2)57. Given that A = 60o, verify that 1 + sin A =(Cos A/2 + Sin A/2)258. If sin θ + cos θ = x and sin θ – cos θ = y, show that x2 + y2 = 259. Show that sin4θ – cos4θ = 1 – 2 cos2θ60. If θ= 45o. Find the value of sec2θ61. Evaluate: cos60 o cos45 o -sin60 o sin45 o62. Find the value of tan15 o.tan25 o.tan30 o tan65 o tan85 o63. If θ is a positive acute angle such that sec θ = cosec60o, then find the value of 2cos2 θ -164. Find the value of sin65-cos25 without using tables.65. If sec5A=cosec(A-36 o). Find the value of A.66. If 2 sin x/2 - 1 =0, find the value of x.67. If A, B and C are interior angles of ΔABC, then prove that cos (B+C)/2 = sinA/268. Find the value of 9sec2A-9tan2A.69. Prove that sin6θ+cos6θ=1-3sin2θcos2θ.70. If 5tanθ-4=0, then find the value of (5sinθ - 4cosθ) (5sinθ + 4cosθ)71. In ABC, 72. In D ABC, right angled at B, if tan a =1/√3 find the value of Sin A cos C + cos A sin C.73. Show that 2(cos4 60 + sin4 30 )- (tan2 60 + cot2 45 ) + 3sec2 30 =1/474. sin(50 +q ) - cos(40 -q ) + tan1 tan10 tan 20 tan 70 tan80 tan89 =175. Given tan A =4/3, find the other trigonometric ratios of the angle A.76. In a right triangle ABC, right-angled at B, if tan A = 1, then verify that 2 sin A cos A = 1.77. In D OPQ, right-angled at P, OP = 7 cm and OQ – PQ = 1 cm. Determine the values of sin Q and cos Q.78. In D ABC, right-angled at B, AB = 24 cm, BC = 7 cm. Determine:(i) sin A , cos A(ii) sin C, cos C79. If �A and �B are acute angles such that cos A = cos B, then show that � A = �B.80. If cot A= 7/8 evaluate: {(1 + sinA )( 1 – sinA)} / {(1+ cosA)(1-cosA)81. In triangle ABC, right-angled at B, if tan A = 1/√3 find the value of :(i) sin A cos C + cos A sin C (ii) Cos A cos C – sin A sin C82. In D ABC, right angled at B, AB = 5 cm and �ACB = 300 Determine the lengths of the sides BC and AC.83. In D PQR, right – angled at Q, PQ = 3 cm and PR = 6 cm. Determine �QPR and �PRQ84. If sin (A-B) = � ,cos(A+B ) = � A+ B = o < A+ B ≤ 90, A > B find A and B85. Evaluate the following: (5cos260 + 4sec230 - tan2 45)/ (sin2 30 + cos2 30)86. If sin 3 A = cos (A – 26), where 3 A is an acute angle, find the value of A.87. Prove the trigonometric identities (1 - cos A)/( 1 – cos A) = (cosec A – cot A)2 88. Prove the trigonometric identities ( 1+ 1/tan2A) (1 + 1/cot2A) = 1/(sin2A- cos4A)89. Prove the trigonometric identities (sec4A – sec2A) = tan4A +tan2A = sec 2 A tan2 A90. Prove the trigonometric identities cotA – tanA = (2cos 2A -1)/ (sinA.cosA)91. Prove the trigonometric identities.(1- sinA +cosA)2 = 2(1+cosA )(1 – sinA)92. If tanA +sinA = m and tanA – sinA=n show that m2 – n2 = 4 93. If x= psecA + qtanA and y= ptan A +q secA prove that x2 – y2 = p2 – q294. If sinA + sin2A = 1 prove that cos2 A + cos4 A =195. Express the following in terms of t-ratios of angles between 0� and 45�.1) sin 85� +cosec 85�2) cosec 69� +cot 69�3) sin 81� +tan 81�4) cos 56� +cot 56�96. [sin (90 -A) sin A]/tan A-1 = - sin� A97. cos cos(90� - ) -sin sin (90� - ) = 098. sin (90� - ) cos (90� - ) = tan /(1 +tan� )99. cosec� (90� - ) -tan� = cos�(90� - ) +cot� 100. If cos /cos = m and cos /sin = n, show that (m� +n�) cos� = n�.If x = r cos sin , y = r cos cos and z = r sin , show that x� +y� +z� = r�.

cosA /1-tanA +sinA / 1-cotA =sinA+cosA

prove that 1/ secA+tanA - 1/cosA = 1/cosA - 1/ secA- tanA

if cosec A+Cot A= p , then proove that cOS A = p2 - 1 / p2+ 1

If cos (81 +θ) = sin (k/3), where 'θ' is an acute angle, then what will be the value ofk?If sec A = x + 1/4x then prove that tan A + secA = 2x or 1/2x

Prove the Identities?

( Sec8A-1)/( Sec4A-1)=Tan8A/Tan2A

If tanA= 4/3. find the value of

2sin-3cosA / 2sinA+3cosA.