How do you verify the identity $sin(x+y)+sin(x-y)=2sinxcosy$ ?

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Answer 1 · 2017-04-30T16:37:40

Please see below.

$sin(x+y)=sinxcosy+cosxsiny$ and

$sin(x-y)=sinxcosy-cosxsiny$

Hence $sin(x+y)+sin(x-y)=sinxcosy+cosxsiny+sinxcosy-cosxsiny$

= $sinxcosy+cancel(cosxsiny)+sinxcosy-cancel(cosxsiny)$

= $2sinxcosy$

How do you verify the identity sin(x+y)+sin(x-y)=2sinxcosysin(x+y)+sin(x-y)=2sinxcosy?