IIT Level Trigonometry – 100 Questions (Set 5: 81–100) | Final Level
81. sinθ + cosθ = a అయితే sin²θcos²θ = ?
Step: sinθcosθ = (a²−1)/2
Square → (a²−1)²/4
Answer = (a²−1)²/4
82. sinθcosθ = a అయితే sin⁸θ + cos⁸θ = ?
Answer = 1 − 4a² + 2a⁴
83. sinθ + cosθ = √2 అయితే sin⁸θ + cos⁸θ = ?
Step: sinθcosθ = 1/2
= 1 − 1 + 1/8
Answer = 1/8
84. sinθcosθ = 1/4 అయితే sin⁸θ + cos⁸θ = ?
= 1 − 1/4 + 1/128
Answer = 97/128
85. tanθ + cotθ = a అయితే sinθcosθ = ?
Answer = 1/a
86. tanθ + cotθ = 3 అయితే sinθcosθ = ?
Answer = 1/3
87. tanθ + cotθ = a అయితే tanθ = ?
x + 1/x = a
x² − ax + 1 = 0
Answer = (a ± √(a²−4))/2
88. tanθ + cotθ = 6 అయితే tanθ = ?
Answer = 3 ± 2√2
89. sinθ + cosθ = a అయితే sin³θ + cos³θ = ?
Answer = a³ − (3a(a²−1))/2
90. sinθcosθ = a అయితే sin³θcos³θ = ?
Answer = a³
91. sinθ + cosθ = √2 అయితే sin³θcos³θ = ?
Answer = 1/8
92. sinθ = 15/17 అయితే cosθ = ?
Answer = 8/17
93. cosθ = 9/41 అయితే sinθ = ?
Answer = 40/41
94. tanθ = 8/15 అయితే sinθ = ?
Answer = 8/17
95. tanθ = 7 అయితే cosθ = ?
Answer = 1/√50
96. sinθ + cosθ ≥ ?
Answer = −√2
97. sinθcosθ ≤ ?
Answer = 1/2
98. tanθ + cotθ ≥ ?
Answer = 2
99. sinθ + cosθ = 2 అయితే possible?
Answer = Not possible
100. sinθcosθ = 1 అయితే possible?
Answer = Not possible
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