化简2sin^2[(π/4)+x]+根号3(sin^x-cos^x)-1

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化简2sin^2[(π/4)+x]+根号3(sin^x-cos^x)-1

化简2sin^2[(π/4)+x]+根号3(sin^x-cos^x)-1
化简2sin^2[(π/4)+x]+根号3(sin^x-cos^x)-1

化简2sin^2[(π/4)+x]+根号3(sin^x-cos^x)-1
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)

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)
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