Question

Verify the identity.

cos (x - y) - cos (x + y) = 2 sin x sin y

Answer 1

cos (x - y) - cos (x + y) = 2 sin x sin y
LHS =cos (x - y) - cos (x + y)
= cosx cosy+sinxsiny -(cosxcosy-sinxsiny)
= cosx cosy+sinxsiny -cosxcosy+sinxsiny
= sinxsiny +sinxsiny
= 2sinx siny
=RHS
Thus given identity is verified.

Answer 2

Gee, thanks!