f(x)=sin^4x+2√3sinxcosx-cos^4x化简

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f(x)=sin^4x+2√3sinxcosx-cos^4x化简

f(x)=sin^4x+2√3sinxcosx-cos^4x化简
f(x)=sin^4x+2√3sinxcosx-cos^4x化简

f(x)=sin^4x+2√3sinxcosx-cos^4x化简
原式=sinx^4-cosx^4+2√3sinxcosx
=sinx^2-cosx^2+√3sin2x
=1-cos2x/2-1+cos2x/2+√3sin2x
=-cos2x+√3sin2x
=2sin(2x-π/6)

f(x)=sin⁴x-cos⁴x+√3sin2x
=(sin²x+cos²x)(sin²x-cos²x)+√3sin2x
=sin²x-cos²x+√3sin2x
=-cos2x+√3sin2x
=√3sin2x-cos2x
=2sin(2x-π/6)
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