cos(x + y) cos(x − y) = cos2 x − sin2 y

I have to show how the problem equals each other by proving the identity.
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1 Answer

cos(x+y)=cos(x)cos(y)-sin(x)sin(y),

cos(x-y)=cos(x)cos(y)+sin(x)sin(y),

cos(x+y)cos(x-y)=cos2(x)cos2(y)-sin2(x)sin2(y)=

cos2(x)cos2(y)-(1-cos2(x))sin2(y)=

cos2(x)cos2(y)-sin2(y)+sin2(y)cos2(x)=

cos2(x)(cos2(y)+sin2(y))-sin2(y)=cos2(x)-sin2(y). QED

by Top Rated User (1.2m points)

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