Question

cosec theta + cot theta = p, then prove that cos theta = p square - 1/p square + 1

Answer 1

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→ By problem,

cosecθ  +cotθ  = p ----(1)

we know that,

cosec²θ - cot²θ  =1

(cosecθ+cotθ) (cosecθ-cotθ) = 1

(cosecθ-cotθ) x p = 1

cosecθ - cotθ = 1/p

cosecθ = 1+p² / 2p

cotθ = p²-1 / 2p

cotθ / cosecθ = p²-1/2p x 2p/ p²-1

cosθ = p²-1/ p²+1

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