f(x) = cos(2x-π/3) + sin^2x - cos^2x的对称轴方程
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f(x) = cos(2x-π/3) + sin^2x - cos^2x的对称轴方程
f(x) = cos(2x-π/3) + sin^2x - cos^2x的对称轴方程
f(x) = cos(2x-π/3) + sin^2x - cos^2x的对称轴方程
f(x) = cos(2x-π/3) + sin^2x - cos^2x
=cos(2x)cos(π/3)+sin(2x)sin(π/3)-cos2x
=(√3/2)sin2x-(1/2)cos2x
=sin(2x-π/6)
所以对称轴2x-π/6=2kπ+π/2
x=kπ+5π/12 k∈Z
f(x)=cos(2x-π/3)+sin²x-cos²x
=cos2xcosπ/3+sin2xsinπ/3-(cos²x-sin²x)
=1/2cos2x+√3/2sin2x-cos2x
=√3/2sin2x-1/2cos2x
=sin(2x-π/6)
令2x-π/6=kπ+π/2 (k∈Z)
得x=kπ/2+π/3 (k∈Z)
对称轴方程为x=kπ/2+π/3 (k∈Z)
化简f(x)=cos(2x-π/3)-cos2x
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