Question

Cos^2x +cos^2y - 2cos x cos . Cos (x+y) = sin^2 (x+y)

Answer 1

Answer:

solved

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)