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Question

Prove that:sin(x+y)sin(xy)=tanx+tanytanxtany

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Solution

L.H.S=sin(x+y)sin(xy)
sinxcosy+cosxsinysinxcosycosxsiny
R.H.S=tanx+tanytanxtany
=sinxcosx+sinycosysinxcosxsinycosy
=sinxcosy+cosxsinycosxcosysinxcosycosxsinycosxcosy
=sinxcosy+cosxsinysinxcosycosxsiny
=L.H.S
Hence L.H.S=R.H.S
Hence proved.

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