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Question

Find
tanθ1cotθ+cotθ1tanθ=cosecθsecθ+1

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Solution

tanθ1cotθ+cotθ1tanθ=secθcosecθ+1

L.H.S=tanθ1cotθ+cotθ1tanθ

=tanθ11tanθ+1tanθ1tanθ

=tan2θ1+tanθ+1tanθ(1tanθ)

=11+tanθ[tan2θ1tanθ]

=1tanθ1tan3θ1tanθ [(a3b3)=(ab)(a2+b2+ab)]

=1tanθ1(tanθ1)tan2θ+1+tanθtanθ

=sec2θ+tanθtanθ

=sec2θtanθ+tanθtanθ

=1cos2θsinθcosθ+1

=1sinθcosθ+1

=secθcosecθ+1

= R.H.S

L.H.S = R.H.S.

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