`(cos x - cos y)^(2) + ( sin x - sin y )^(2) = 4 sin^(2)((x-y)/2)`

Explanation

` L.H.S = ( cos x - cos y )^(2) + ( sin x - sin y)^(2)`
` = [2 sin. ((x+y)/2) sin.((y-x)/2)]^(2)`
`+ [ 2 cos ((x+y)/2) sin ((x-y)/2)]^(2)`
` = 4 sin^(2) ((x+y)/(2)) sin^(2).((x-y)/(2))`
` + 4 cos ^(2) ((x+y)/2) sin^(2) ((x-y)/2)`
` = 4 sin^(2) ((x-y)/2) [ sin^(2)((x+y)/2)+ cos^(2)((x+y)/2)]`
` = 4 sin^(2) ((x-y)/2) (1)`
` = 4 sin ^(2). (x-y)/2 ` = R.H.S