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Question

Prove the following trignometric identities:

cos θ1sin θ=1+sin θcos θ


Solution

We know ,

cos2θ+sin2θ=1

So, Multiplying both numerator and denominator by  (1+sinθ), we have

cos θ1sin θ=cos θ(1+sin θ)(1sin θ)(1+sin θ)

=cos θ(1+sin θ)(1sin2θ)

= cos θ(1+sin θ)cos2θ

=1+sin θcos θ

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