# 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�.

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1.its given that AB=24cm and BC=7cm

so,using pythagoras theorem (BC)2=(AB)2+(BC)2

(BC)2=(24)2+(7)2

BC=25cm

sinA=BC/BC=7/25

cosA=AB/AC=24/25

SIN C=AB/AC=24/25

COS C=BC/AC=7/25

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