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Mathematics

Solved Exercises

- Class 09



Unit-4 - Trigonometry

Compound Angles

  1. Find the value of sin15°
  2. Find the value of tan15°
  3. Find the value of cos15°
  4. Find the value of sin105°
  5. Find the value of sin135°
  6. Find the value of tan75°
  7. Find the value of cot15°
  8. Prove that: sin65° + cos65° = √2 cos20°
  9. Prove that: cos18° - sin18° = √2 sin27°
  10. Prove that: cos40° + sin40° = √2 cos5°
  11. Prove that: cos55° + sin55° = √2 cos10°
  12. If α +β= 45°, then prove that: (tanα +1)(tanβ +1) = 2
  13. If α+ β= π/4, prove that: (cotα -1) (cotβ-1) =2
  14. If A+B = 45°, prove that: cotA.cotB -cotA -cotB =1
  15. If A and B are two acute angles of a right angled triangle ABC, prove that: tanA.tanB =1
  16. If α +β= 45°, then prove that: cotβ(cotα -1) - cotα = 1
  17. If tan(α +β) = 1 and tanα = 3, prove that: tanβ = -1/2.
  18. If tan(α +β) = 33 and tanα = 3, prove that: tanβ = 3/10.
  19. If tanA = m and tanB = 1/m, find the value of (A+B).
  20. If sinA = 4/5 and cosB = 5/13, find the value of sin(A+B).
  21. If tanA= 5/6 and tanB = 1/11, prove that: A+B = 45°
  22. If A+B+C =Ï€ and cosA = cosB.cosC, prove that: tanA = tanB + tanC.
  23. If cot(A+B)= 8 and cot(A-B)= 4, find the value of cot 2A and cot2B.
  24. If tan(A+B) =2/3 and tan(A-B)= 2/5, then find the values of tan2A and tan2B.
  25. How to find the value of tan2A and tan2B when tan(A+B) and tan(A-B) are given?
  26. If cos(A+B) = 12/13 and cos(A-B) = 5/13, then find the values of sin2B and cos2B.
  27. If sin(A+B) =4/5 and sin(A-B)= 3/5, then find the values of sin2A and cos2A.
  28. If sinA=3/5 and sinB=12/13, find the given values.
  29. If cosA=1/7 and cosB =13/14, find the values of sin(A-B) and cos(A-B).
  30. If sinα =15/17 and cosß =12/13 , then find the values of sin(α +ß) , cos( α+ß) and tan(α +ß).
  31. If tan(A-B) = 16/63 and tanA = 3/4 then show that tanB= 5/12.
  32. Prove that: sin(45° +A) + cos(45° +A) =√2 cosA
  33. Prove that: cos(45°+A) - sin(45°-A) = 0
  34. Prove that: sin²(45°+Θ) +sin²(45°-Θ) = 1
  35. Prove that: 2cos(45°+Θ).cos(45°-Θ) = cos²Î˜- sin²Î˜
  36. Prove that: 2sin(45°+Θ).sin(45°-Θ) = cos²Î˜ -sin²Î˜
  37. Prove that: sin(45°+A).sin(45°-A) = 1/2(cos²A -sin²A)
  38. Prove that: sin5Θ -sin3Θ +sin2Θ = 4sinΘ.cos3Θ/2.cos5Θ/2
  39. Find the value of sin(13Ï€/12).
  40. Prove that: 1- 2sin²(45°-α) = 2sinα.cosα
  41. Prove that: sin(45°+A) -cos(45°-A)= 0
  42. Prove that: (tan4A-tan3A)/(1+ tan4A.tan3A) = tanA
  43. Prove that: tan²A -tan²B = {sin(A+B).sin(A-B)}/ cos²A.cos²B
  44. Prove that: (cos20°- sin20°)/(cos20° +sin20°} = tan25°
  45. Prove that: (cos40° -sin40°)/(cos40°+sin40°) = tan5°
  46. Prove that: 2tan50° +tan20° = cot20°
  47. Prove that: 1- tan35°.tan10° = tan35° + tan10°
  48. Prove that: tan29° +tan16° +tan29°.tan16° = 1
  49. Prove that: cot22°.cot23° -cot22° -cot23° = 1
  50. If TanA= x/(x+1) and TanB = 1/(2x+1), then prove that: A+B = π/4.
  51. If cosA= 1/√17 and cosB = 3/√34, then show that: A+B = 3Ï€/4.