Question

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

Answer 1

Please see below.

Explanation:

`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`