Cos^2x +cos^2y - 2cos x cos . Cos (x+y) = sin^2 (x+y)
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Step-by-step explanation:
RHS = sin²(x+y) = {sinxcosy + cosxsiny}²
= sin²xcos²y + cos²xsin²y + 2 sinxcosy cosxsiny
= cos²x(1-cos²y) + cos²y(1-cos²x) + 2 sinxcosy cosxsiny
= cos²x + cos²y - 2cos²xcos²y + 2 sinxcosy cosxsiny
= cos²x + cos²y - 2cosxcosy {cosxcosy -sinxsiny}
= cos²x + cos²y - 2cosxcosy cos(x+y)
= LHS
cos²x + cos²y - 2cosxcosy cos(x+y) = sin² (x+y)
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