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Syllabus

If cosec theta - cot theta = 1/3 then find the value of ( cosec theta + cot theta)

if tan

~~o~~+sin~~o~~= m,tan~~o~~-sin~~o~~=n,prove that m^{2}-n^{2}=4root mnHow to make working model on trigonometry?

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

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 !!!!!!!!!!!!!

^{2}A - cosec^{2}A=2sin^{2}A-1/sin^{2}A cos^{2}Aif secA =x+ (1/4x), prove that secA + tanA =2x or 1/2x

rply fst!!!

a person had a number of toys to distribute among children . at first he gave 2 toys to each child , then 4 , then 5 ,and then 6 , but was always left with one . but if he had given 7 toys to each child , no toys would have been left with him . what is the smallest number of toys that he had?

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

If sec (theta) + tan (theta) = 7 then find the value of sec (theta) - tan (theta)

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

Plzz answer fast

If sec(theta)=x+1/4x, prove that sec(theta)+tan(theta)=2x or 1/2x

please answer my ques. Thanks in advance.

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.

In the given figure, if DE is parallel to BC, AE=8cm, EC=2cm and BC=6cm, then find DE.

find the value of sin30 geometrically

Prove That: cos

^{3}theta+ sin^{3}theta/cos theta+sintheta+cos

^{3}theta-sin^{3}theta/costheta-sinthetaif sec theta+tan theta =p ,prove that sin theta = (p square- 1) / (p square + 1)

(sec A-cos A).(cot A+tan A)=sec A.tanA

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

^{3}𝜃 + 𝑐𝑜𝑠^{3}𝜃/sin𝜃 + cos𝜃+(sin𝜃cos𝜃)=1if A,B,c are interior angles of triangle ABC then show that sin (B+C/2) = cos A/2

√(7-x). tan C + √(7+x). cot A-14cos A+21sin C+ √[49+ x^(2)]. cos B

Find the value of sin60 geometrically

^{2}A = 1+cot^{2}AIf acosx-bsinx =c, prove that asinx + bcosx = +- root(a

^{2}+b^{2}-c^{2})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

^{2}theta - 3 cos theta + 2 / sin^{2}theta = 1If 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

if tan^2A+cot^2A=2 then tan^3A +cot^3A=

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.

Prove that:(sin theta + cosec theta)

^{2}+ (cos theta + sec theta)^{2}= 7 + tan^{2}theta + cot^{2}thetaif 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

^{2}A.tanA + cos^{2}A.cotA + 2sinA.cosA = tanA+cotAif cosA +sinA=root2cosA show that cosA -sinA=root2 sina

an equilateral triangle is inscribed in a cirle of radius 6 cm.Find its sides

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. 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/root3thetaevaluate root 7-x.tan C+cot A-14 cos A+21 sin C+root 49+x^2.cosb

prove sin theta-2sin cube theta/2cos cube theta-cos theta=tan theta

solve (cosec theta-sin theta)(sec theta - cos theta) = 1tan theta + cot theta

^{3}A-cos^{3}A)/(sinA+cosA) + sinAcosA = 1If cosec theta + cot theta= p Prove that cos theta = p

^{2}-1 by p^{2}+1in triangle ABC, C=90, AB=x units and AC=3 units

evaluvate:

x. cosB. tanA+x

^{2}sinA. secB+sinCGiven that sinθ + 2cosθ = 1, then prove that 2sinθ – cosθ = 2.

^{2 }theta - cos^{2 }theta =sin^{2}theta (sec^{2 }theta - 1)(1+ cot A - cosec A) (1+ tan A + sec A) = 2

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

prove that tan+sec-1/tan-sec+1 =1+sin/cos

2)If sinA = root 3/2, find the value of 2cot^{2}A-1.Prove that:- sin

^{6}theta + cos^{6}theta = 1-3sin^{2}theta.cos^{2}thetaIf Sin + Cos = p and Sec + Cosec = q, show that q(p2 – 1) = 2p.prove that cotA + cosecA -1/ cotA - CosecA + 1 = 1 + cosA - sinA

if 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

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 examgiven 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

If

^{cos(theta) - sin(theta)}/_{cos(theta) + sin(theta) }=^{1 - (root)3}/_{1 + (root)3}Find (theta)

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

Prove that:-

(Whole root)CosecA+1

--------------- = SecA + TanA

CosecA-1

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

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

SHOW THAT

1/1+sin

^{2}A +1/1+cos^{2}A +1/1+sec^{2}A +1/cosec^{2}A=2if cosec A+Cot A= p , then proove that cOS A = p2 - 1 / p2+ 1

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

If sec A = x + 1/4x then prove that tan A + secA = 2x or 1/2x

if sin theta - cos theta = 1/2, find the value of sin theta+ cos theta

Prove the Identities?

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