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Question

Show that sin(x+y)sin(xy)=tanx+tanytanxtany

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Solution

RHS tanx+tanytanxtany

=sinxcosx+sinycosysinxcosxsinycosy

=sinxcosy+sinycosxcosxcosysinxcosysinycosxcosxcosy

=sinxcosy+sinycosxsinxcosysinycosx

=sin(x+y)sin(xy)

Hence proved.

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