IIT Level Trigonometry – 100 Questions (Set 3: 41–60)

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41. sinθ + cosθ = a అయితే sin²θcos²θ = ?
Step: sinθcosθ = (a²−1)/2
Square → (a²−1)²/4
Answer = (a²−1)²/4

42. sinθcosθ = a అయితే sin⁴θ + cos⁴θ = ?
Answer = 1 − 2a²

43. sinθ + cosθ = √2 అయితే sin⁴θ + cos⁴θ = ?
Step: sinθcosθ = 1/2
= 1 − 2(1/4)
Answer = 1/2

44. sinθ + cosθ = 1 అయితే sin⁴θ + cos⁴θ = ?
Step: sinθcosθ = 0
Answer = 1

45. sinθcosθ = 1/4 అయితే sin⁶θ + cos⁶θ = ?
Step: = 1 − 3(1/16)
Answer = 13/16

46. sinθ + cosθ = a అయితే sin⁶θ + cos⁶θ = ?
Answer = 1 − 3[(a²−1)/2]²

47. tanθ + cotθ = a అయితే sinθcosθ = ?
Answer = 1/a

48. sinθcosθ = a అయితే tanθ + cotθ = ?
Answer = 1/a

49. tanθ + cotθ = 4 అయితే tanθ = ?
Let x = tanθ
x + 1/x = 4
x² − 4x + 1 = 0
Answer = 2 ± √3

50. tanθ + cotθ = 5 అయితే tanθ = ?
x + 1/x = 5
x² − 5x + 1 = 0
Answer = (5 ± √21)/2

51. sinθ + cosθ = a అయితే sin³θ + cos³θ = ?
Answer = a³ − (3a(a²−1))/2

52. sinθcosθ = a అయితే sin³θcos³θ = ?
Answer = a³

53. sinθ + cosθ = √2 అయితే sin³θcos³θ = ?
Step: sinθcosθ = 1/2
= (1/2)³
Answer = 1/8

54. sinθ = 5/13 అయితే cosθ = ?
Answer = 12/13

55. cosθ = 3/5 అయితే sinθ = ?
Answer = 4/5

56. tanθ = 3/4 అయితే sinθ = ?
Answer = 3/5

57. tanθ = 3 అయితే cosθ = ?
Answer = 1/√10

58. tanθ = 1 అయితే sinθ + cosθ = ?
Answer = √2

59. sinθ + cosθ ≥ ?
Answer = −√2

60. sinθcosθ ≤ ?
Answer = 1/2

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Shaktimatha Learning | IIT Advanced Series