Question

求化简f(x)=sin^2x+2根号3sin(x+π/4)cos(x-π/4)-cos^2x-根号3

还有为什么我看不到回复orz……

Answer 1

利用三角函数积化和差公式
sinAcosB=0.5[sin(A+B)+sin(A-B)]
和倍角公式cos2A=cos²A-sin²A
原式=sin²x+√3[sin2x+sin(π/2)]-cos²x-√3
=-cos2x+√3sin2x
=2[-sin(π/6)cos2x+cos(π/6)sin2x]
=2sin[2x-(π/6)]
不明白的可以追问，如果有帮助，请选为满意回答！

Answer 2

f(x)=sin^2x+2根号3sin(x+π/4)cos(x-π/4)-cos^2x-根号3

=sin^2x+根号3* sin(2x+π/2)-(1-sin^2x)-根号3
=2sin^2x-1-根号3-根号3* cos(2x)
=2sin^2x-1-根号3-根号3*（1-2sin^2x）
=2sin^2x-1-根号3-根号3+2根号3sin^2x
=（2+2根号3）sin^2x -2根号3-1

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