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1-(cos(x)+sin(x))(cos(x)-sin(x))=2sin^2(x)

foil out the center

I get

1-cos^2(x)-cos(x)sin(x)+cos(x)sin(x)+sin^2(x)

the -cos(x)sin(x)+cos(x)sin(x) cancels to 0 leaving

1-cos^2(x)-sin^2(x)

then I'm lost...

I know I can switch 1-cos^2(x) to sin^2(x) but that doesn't help because I get

sin^2(x)-sin^2(x)=0

where am i going wrong?