If cosecθ + cotθ = n, then find cosecθ.

{n + (1/n)}

1/2{n + (1/n)}

1/3{n + (1/n)}

1/4{n + (1/n)}

If cosecθ + cotθ = n, then find cosecθ. Correct Answer 1/2{n + (1/n)}

Given:

cosecθ + cotθ = n ----(1)

Identity used:

cosec²θ - cot²θ = 1

Explanation:

cosec2θ - cot2θ = 1

⇒ (cosecθ + cotθ) (cosecθ - cotθ) = 1

⇒ n × (cosecθ - cotθ) = 1

⇒ (cosecθ - cotθ) = 1/n ----(2)

On adding equation (1) & (2), we get

⇒ 2cosecθ = {n + (1/n)}

∴ cosecθ is 1/2{n + (1/n)}.

Feb 20, 2025

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