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Question

Prove that
(secθ+cosθ)(secθcosθ)=tan2θ+sin2θ

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Solution

L.H.S=(secθ+cosθ)(secθcosθ)

=sec2θcos2θ

=1+tan2θcos2θ[1+tan2θ=sec2θ]

=tan2θ+1cos2θ

=tan2θ+sin2θ[sin2θ+cos2θ=1]

=R.H.S

(secθ+cosθ)(secθcosθ)=tan2θ+sin2θ

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