CDS 2026 · PYQ · Trigonometry · medium
For the next two (02) items that follow:
12(tanθ + cotθ) = 25, where 45° < θ < 90°
What is the value of (cosecθ + secθ)?
Answer
The correct answer is B: 35/12. cosecθ + secθ = 1/sinθ + 1/cosθ = (sinθ + cosθ)/(sinθ cosθ). Now (sinθ + cosθ)² = 1 + 2sinθcosθ = 1 + 24/25 = 49/25, so sinθ + cosθ = 7/5.
- A.4
- B.35/12✓ Correct
- C.25/12
- D.2
cosecθ + secθ = 1/sinθ + 1/cosθ = (sinθ + cosθ)/(sinθ cosθ). Now (sinθ + cosθ)² = 1 + 2sinθcosθ = 1 + 24/25 = 49/25, so sinθ + cosθ = 7/5. Therefore cosecθ + secθ = (7/5)/(12/25) = (7/5) × (25/12) = 35/12.
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