Question

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

Answer 1

Answer:

Step-by-step explanation:

LHS = (cosx + cosy)² + (sinx - siny)²

       = cos²x + cos²y + 2 cosx cosy + sin²x + sin²y - 2 sinx siny

       = cos²x + sin²x + cos²y + sin²y + 2 cosx cosy - 2 sinx siny

       = 1 + 1 + 2 (cosx cosy - sinx siny)

       = 2 + 2 cos (x + y)

       = 2 (1 + cos (x + y) )

       = 2 (1 + 2 cos²(x+y)/2 - 1)

       = 2  (2 cos²(x+y)/2)

        = 4 cos²(x+y)/2