化简2sin^2[(π/4)+x]+根号3（sin^x-cos^x）-1
问题描述：
化简2sin^2[(π/4)+x]+根号3（sin^x-cos^x）-1
答
2sin^2[(π/4)+x]+根号3（sin^x-cos^x）-1
=2sin^2[(π/4)+x]-1+√3（sin^x-cos^x）
=-cos[2(π/4)+x)] +√3(-cos2x)
=sin(2x) - √3cos2x
=2sin(2x-π/3)
满意请及时采纳！有疑问可追问！
答
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)