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If cosecθ = 5/3, then evaluate (sec²θ – 1) × cot²θ × (1 + cot²θ).

SSC · 2024 · Quantitative Aptitude
Question:
If cosecθ = 5/3, then evaluate (sec²θ – 1) × cot²θ × (1 + cot²θ).

Options

(1) 25/16
(2) 9/16
(3) 25/9
(4) 4/5
Answer: (3) 25/9

Explanation:
cosecθ = 5/3, so sinθ = 3/5, cosθ = 4/5. Calculate each term and multiply.

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