Prove that: (cosx - cosy)² + (sinx - siny)² = 4sin²(x-y)/2

LHS = (cosx - cosy)² + (sinx - siny)²
= cos²x + cos²y - 2cosxcosy + sin²x + sin²y - 2sinxsiny
= (cos²x + sin²x) + (cos²y + sin²y) - 2(cosxcosy + sinxsiny)
= 1 + 1 - 2cos(x - y)
= 2(1 - cos(x - y))
= 4sin²(x - y)/2 = RHS (∵ 1 - cos2x = 2sin²x)
Hence proved