Question

(cosx - cosy )square + (sinx - siny)square to prove 4cos square (x+y)/2 ​

Answer 1

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

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

by substituting this two equations,

(-2 sin (x+y)/2 sin (x-y)/2)²+

(2cos (x+y)/2 sin (x-y)/2)²