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Question

Prove the following:
(tanθ+secθ1)tanθsecθ+1)=1+sinθcosθ.

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Solution

LHS
tanθ+secθ1tanθsecθ+1

tanθ+secθ(sec2θtan2θ)tanθsecθ+1

tanθ+secθ(secθtanθ)(secθ+tanθ)tanθsecθ+1

tanθ+secθ(1secθ+tanθ)tanθsecθ+1

tanθ+secθsinθcosθ+1cosθ1+sinθcosθ

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