f(x)=2[(sinx)^4+(cosx)^2]+cos²2x-3
=2[(sin²x+cos²x)²-2sin²xcis²x]+cos²2x-3
=2(1-2sin²xcos²x)+cos²2x-3
=2-(2sinxcosx)²+cos²2x-3
=-sin²2x+cos²2x-1
=-cos4x-1