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Question

Prove that:
tan(α+β)+tan(αβ)=sin2α1sin2αsin2β

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Solution

Now,
tan(α+β)+tan(αβ)
=sin(α+β)cos(α+β)+sin(αβ)cos(αβ)
=sin(α+β).cos(αβ)sin(αβ).cos(α+β)cos(α+β).cos(αβ)
=sin(α+β+αβ)cos2αsin2β [ Since cos(α+β).cos(αβ)=cos2αsin2β]
=sin2α1sin2αsin2β [ Since cos2α=1sin2α]

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