化简2sin^2[(π/4)+x]+根号3（sin^x-cos^x）-1

题目

化简2sin^2[(π/4)+x]+根号3（sin^x-cos^x）-1

答案

2sin^2[(π/4)+x]+根号3（sin^x-cos^x）-1
=-(1-2sin^2[(π/4)+x)-√3cos2x
=-cos(π/2+2x)-√3cos2x
=sin2x-√3cos2x
=2[1/2*sin2x-√3/2*cos2x]
=2sin(2x-π/3)