Answer:
Step-by-step explanation:
(cos x+cos y)²+(sin x-sin y)²
=cos²x+cos²y+2 cos x cos y+sin²x+sin²y-2 sin x sin y
=(cos ²x+sin ²x)+(cos ²y+sin ²y)+2(cos xcos y-sin x sin y)
=1+1+2cos(x+y)
=2+2 cos (x+y)
=2[1+cos (x+y)]
=2 *2cos²((x+y)/2)
[tex]=4 cos^2(\frac{x+y}{2} )[/tex]
