化简：cos4x－2sinxcosx－sin4x

化简：cos4x－2sinxcosx－sin4x
化简：cos4x－2sinxcosx－sin4x

化简：cos4x－2sinxcosx－sin4x
f(x)=(cos²x+sin²x)(cos²x-sin²x)-2sinxcosx
=1×cos2x-sin2x
=√2(cos2x×√2/2-sin2x×√2/2)
=√2(cos2xcosπ/4-sin2xsinπ/4)
=√2cos(2x+π/4)