Question

Verify the identity.

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

Answer 1

is this a recipricol identity??

Answer 2

cos (x - y) = cosx cosy +sinxsiny
cos (x +y) = cosx cosy -sinxsiny

Answer 3

thus
cos (x - y) - cos (x + y) = (cosx cosy +sinxsiny ) - (cosx cosy -sinxsiny )
=cosx cosy +sinxsiny -cosx cosy +sinxsiny =2sinxsiny