CDS 2026 · PYQ · Trigonometry / Identities · easy
If cosθ/(1 − sinθ) + cosθ/(1 + sinθ) = 4, then which one of the following is a value of (tan²θ + cot²θ)?
Answer
The correct answer is B: 10/3. Combining the LHS: cosθ[(1 + sinθ) + (1 − sinθ)]/[(1 − sinθ)(1 + sinθ)] = 2cosθ/cos²θ = 2/cosθ = 2secθ. So 2secθ = 4, giving secθ = 2, hence cosθ = 1/2 and sinθ = √3/2.
- A.5/3
- B.10/3✓ Correct
- C.4
- D.5
Combining the LHS: cosθ[(1 + sinθ) + (1 − sinθ)]/[(1 − sinθ)(1 + sinθ)] = 2cosθ/cos²θ = 2/cosθ = 2secθ. So 2secθ = 4, giving secθ = 2, hence cosθ = 1/2 and sinθ = √3/2. Then tanθ = √3 and cotθ = 1/√3. So tan²θ + cot²θ = 3 + 1/3 = 10/3.
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