Back
Optional

Mathematics

Solved Exercises

- Class 09



Unit-4 - Trigonometry

Trigonometric Values

  1. Prove that: sinα / (1+cosα) + (1+cosα) / sinα = 2cosecα
  2. Find the value of: cosec(-1485°)
  3. If sinθ - cosθ = 0, Find the value of 'θ'.
  4. If sinA = 12/13 , find cosA and tanA.
  5. If sinΘ - cosΘ = 0. Find the value of cosecΘ.
  6. If 6 sin^2 Θ - 5 cosΘ = 0, find the value of cosΘ.
  7. If 3 sinA + 4 cosA = 5, find the value of tanA.
  8. If cosx = 1/√10 , then prove that sec^2x - tan^2x =1
  9. If tanA+sinA =p and tanA-sinA= q, prove that: p^2-q^2 = 4√(pq)
  10. If sinα= cosβ = √3/2, then prove that: tan(α -β) = (tanα - tanβ)/ (1+ tanα. tanβ)
  11. If sin4A = cos2A, find the value of A.
  12. If sinA=3/5 and cosB= 5/13, find the value of sinA.cosB + cosA.sinB
  13. If 3sinΘ +4cosΘ =5, show that: sinΘ = 3/5
  14. If sin^2Θ - cos^2Θ = 0, prove that: sinΘ = 1/√2
  15. Find the value: sin^2 30°× cos^2 45° + tan^2 60°×cosec^2 90°
  16. If A = 2B = 3C = 90°, find the value of cos^2 A - cot^2 B + cosec^2 C
  17. Find the value: 2 sin60° + tan^2 30° + tan^2 45° - tan60° + cos^2 30°F
  18. Find the value: Tan^2 150° -sin^2 120° +sin^2 135° + cos^2 120°
  19. Find the value: √3sin60° + √2cos45° + 8cos60°
  20. If sinx-cosx = 0, Find the value of cosecx - cotx.
  21. Prove that: √45 +√12 +√15 +√3 . Tan30°= 7
  22. Prove that: cos25°.cos65° - sin25°.sin65° = 0
  23. Prove that: tan^2 60° +4cos^2 45° +3sec^2 30° = 9
  24. Find the value: 3tan^2 π^c/4 - sin^2 π^c/3 -1/4 cot^2 π^c/6 +1/4 sec^2 π^c/6
  25. Find the value: 2 tan^2 π/4 - 3 sin^2 π/3 + 3 cos^2 π/6
  26. Find the value: tan^2 30° +2sin60° + tan^2 45° - tan60° +cos^2 30°
  27. Find the value of: sin420°.cos390° + cos(-300°).sin(-330°)
  28. Find the value of cosec(-570°)
  29. Find the value of: (2 +tan30°) /(1- tan^2 30°
  30. Prove that: (1+ tan30°)/(1- tan30°) = 2+ √3
  31. Prove that: (cosπ/3 - sinπ/3) (cosπ/3 + sinπ/3) = -1/2
  32. If α=0°, β=30°, γ=45° and Θ=90°, prove: tan^2 α +tan^2 β +tan^2 γ +sin^2 Θ =7/3
  33. Prove that: sin112° + cos74° - sin68° + cos106° = 0
  34. Prove that: cos π/8 + cos 3π/8 + cos 5π/8 + cos 7π/8 = 0
  35. Prove that: tan65° + cos35° = cot25° + sin55°
  36. Find the value of: sin^2 3Ï€/4 + 2tan^2 3Ï€/4 -sec^2 3Ï€/4 - cos^2 3Ï€/4
  37. Find the value of: 3tan^2 150° + 4/3 cos^2 150° -1/2 sec^2 135° +1/3 sin^2 120°
  38. Find the value of: tan20°.tan45°.tan70°.tan60°
  39. Find the value of: cos390° .sin330° - sin510°.cos570°
  40. Find the value of: sin330°.cos300° + cos390°.sin420°
  41. Find the value of: [ tan(180-Θ). cot(90-Θ). cos(360-Θ) ] [ sin(-Θ). tan(90+Θ). tan(180-Θ)]
  42. Prove that: sin^2 π/8 + sin^2 3π/8 + sin^2 5π/8 + sin^2 7π/8 = 0
  43. Prove that: sin π/8. sin 7π/8 - cos 3π/8. cos 5π/8 = 2 sin^2 π/8
  44. Prove that: sin20° + sin40° + sin200° + sin220° = 0
  45. Find the value of x: Cosec(90° +Θ) + xcosΘ.cot(90°+Θ) = sin(90° + Θ)
  46. Prove that: 2cos 2Ï€/3 . Cot 3Ï€/4 + sin5Ï€/6;. Tan 3Ï€/4 = 1/2
  47. Prove that: tan^2 A.tan^2 (90°-A) - cos^2(90°-A). Cot^2 A = sin^2 A
  48. Prove that: cos^2 7π/8 + cos^2 5π/8 + cos^2 3π/8 + cos^2 π/8 = 2
  49. Prove that: sin^2 135° +cos^2 120° - sin^2 120° + tan^2 150° = 1/3
  50. Prove that: cot π/20 . Cot 3π/20 .cot5π/20 . Cot7π/20 . Cot 9π/20 = 1
  51. Find the value of x: Tan(180° -Θ).cot(90° +Θ) +x cos(90° +Θ).cos(90°-Θ) = sinΘ.sin(180° -Θ)
  52. Find the value of x: Sin(90°+Θ).sin(90°-Θ) = xsin(-Θ).cos(-Θ) + cos(90°-Θ).cos(90°+Θ)
  53. Find the value of α: x cotα. Tan(90°+α) = tan(90°+α).cot(180°-α) + xsec(90°+α).cosecα
  54. Find the value of x: x cos(90°+A). Cos(90°- A) -sinA.sin(180°-A) = cot(90° +A).tan(90°-A)
  55. Find the value of x: x sec(90°+Θ). CosecΘ + tan(90°+Θ). Cot(180°+ Θ) = xcotΘ. Tan(90°+Θ)
  56. Prove that: x.tan(180° +A).cot(90°+A) = cot(270°-A) .tan(360° -A) +cosecA(90°-A).cosec(90°+A)
  57. If sin(A+B-C) = cos(C+A-B) = tan(B+C-A) = 1. Find the value of A,B and C.
  58. Solve the ∆PQR, when angleQ= 90°, angleP=60° and the sides opposite to angleP is 2√3 cm.
  59. Prove that: If tan25° = x, show that: (Tan205° -tan115°)/(tan245° +tan335°) = (1+x²)/(1-x²)
  60. Find the value of: Sec^2 π/4. Sec^2 π/3 (cosec π/6 - cosec π/2)
  61. Find the value of: cos20° + cos40° +cos140° +cos160°
  62. Find the value of x: Cosec(90° +Θ) + xcosΘ.cot(90°+Θ) = sin(90° + Θ)