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Question

Prove the following trignometric identities:

1cos θ1+cos θ=cosec θcot θ

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Solution

We know ,

cos2θ+sin2θ=1

Multiplying both numerator and denominator by (1cosθ), we have


1cos θ1+cos θ
= (1cos θ)(1cos θ)(1+cos θ)(1cos θ)
= (1cos θ)2(1cos2 θ)
= (1cos θ)2(sin2 θ)
= (1cos θ)sin θ
= 1sin θ - cos θsin θ

= cosec θcot θ


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