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Question

Prove the following trignometric identities:

cosec θ1cos2θ=1


Solution

We know ,

sin^2θ+cos^2θ=1
sin^2θ+cos^2θ=1

So,

cosecθ√1−cos^2θ
=cosecθ√sin^2θ
cosecθ1−cos2θ−−−−−−−−√cosecθsin^2θ−−−−−
√cosecθsinθ
=cosecθsinθ

= (1/sinθ) sinθ

= 1

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