Prove that - (cos x - cos y) 2 + (sin x - sin y) 2 = 4 sin 2 [(x-y)/2]

Question

Philoid · Accepted Answer

We know that-

L.H.S = (cos x - cos y)² + (sin x - sin y)²

= 4 sin²[(x-y)/2]×1 [∵ sin²x + cos²x = 1]

= 4 sin²[(x-y)/2]

= R.H.S

Hence, L.H.S = R.H.S…Proved

Prove that -(cos x - cos y)2 + (sin x - sin y)2 = 4 sin2[(x-y)/2]