Question

Prove that cos²x+cos²y-2cosx.cosy.cos(x+y)=sin²(x+y)

Answer 1

cos^2x+cos^2y-2cosx.cosy.cos(x+y)
cos^2x+1-sin^2y-2cosx.cosy.cos(x+y)
1+cos^2x-sin^2y-2cosx.cosy.cos(x+y)
1+cos(x+y).cos(x-y)-2cosx.cosy.cos(x+y)
1+cos(x+y){ cos(x-y)-2cosx.cosy }
1+cos(x+y){ cosx.cosy-sinx.siny-2cosx.cosy }
1+cos(x+y){ -cosx.cosy + sinx.siny }
1-cos(x+y){ cosx.cosy-sinxsiny }
1-cos(x+y).cos(x+y)
1-cos^2(x+y)
sin^2(x+y).

Answer 2

Step-by-step explanation:

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