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