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Question

Prove that 1+secθsecθ=sin2θ1cosθ

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Solution

We need to prove 1+secθsecθ=sin2θ1cosθ

Taking R. H. S. =sin2θ1cosθ

=1cos2θ1cosθ

=(1cosθ)(1+cosθ)(1cosθ)

=1+cosθ

Now taking L.H.S. =1+secθsecθ

=1+1cosθ1cosθ

=cosθ+1cosθ1cosθ

=1+cosθ

L.H.S. = R.H.S.
Hence, it proved.

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