SSC CHSL 2025 · PYQ · Trigonometry · medium
If, 2 × sinq × cos(90° − q) = (1/2), such that 0° < q < 90°, then find the value of cot²2q + cos²3q.
Answer
The correct answer is D: 1/3. cos(90°−q) = sinq, so 2sin²q = 1/2, sin²q = 1/4, sinq = 1/2, q = 30°. Then cot²(60°) + cos²(90°) = (1/√3)² + 0 = 1/3.
- A.1/5
- B.1/2
- C.1/7
- D.1/3✓ Correct
cos(90°−q) = sinq, so 2sin²q = 1/2, sin²q = 1/4, sinq = 1/2, q = 30°. Then cot²(60°) + cos²(90°) = (1/√3)² + 0 = 1/3.
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