IIT Level Trigonometry – 100 Questions (Set 4: 61–80)

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61. sinθ + cosθ = a అయితే sin⁴θ + cos⁴θ = ?
Step: sinθcosθ = (a²−1)/2
= 1 − (a²−1)²/2
Answer = 1 − (a²−1)²/2

62. sinθcosθ = a అయితే sin⁶θ + cos⁶θ = ?
Answer = 1 − 3a²

63. sinθ + cosθ = √2 అయితే sin⁶θ + cos⁶θ = ?
Step: sinθcosθ = 1/2
= 1 − 3/4
Answer = 1/4

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

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

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

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

68. tanθ + cotθ = 6 అయితే tanθ = ?
x² − 6x + 1 = 0
Answer = 3 ± 2√2

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

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

71. sinθ + cosθ = 1 అయితే sin³θ + cos³θ = ?
Step: sinθcosθ = 0
Answer = 1

72. sinθ + cosθ = 0 అయితే sin³θ + cos³θ = ?
Answer = 0

73. sinθ = 8/17 అయితే cosθ = ?
Answer = 15/17

74. cosθ = 7/25 అయితే sinθ = ?
Answer = 24/25

75. tanθ = 12/5 అయితే sinθ = ?
Answer = 12/13

76. tanθ = 5 అయితే cosθ = ?
Answer = 1/√26

77. sinθ + cosθ max?
Answer = √2

78. sinθcosθ max?
Answer = 1/2

79. tanθ + cotθ min?
Answer = 2

80. sinθ + cosθ = 2 అయితే possible?
Answer = Not possible

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