已知函数f(x)=2sin(x-兀/6)cosx+2cos2x.求f(x)的单调递区间?急用
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![已知函数f(x)=2sin(x-兀/6)cosx+2cos2x.求f(x)的单调递区间?急用](/uploads/image/z/15085227-3-7.jpg?t=%E5%B7%B2%E7%9F%A5%E5%87%BD%E6%95%B0f%28x%29%3D2sin%28x-%E5%85%80%2F6%29cosx%2B2cos2x.%E6%B1%82f%28x%29%E7%9A%84%E5%8D%95%E8%B0%83%E9%80%92%E5%8C%BA%E9%97%B4%3F%E6%80%A5%E7%94%A8)
已知函数f(x)=2sin(x-兀/6)cosx+2cos2x.求f(x)的单调递区间?急用
已知函数f(x)=2sin(x-兀/6)cosx+2cos2x.求f(x)的单调递区间?急用
已知函数f(x)=2sin(x-兀/6)cosx+2cos2x.求f(x)的单调递区间?急用
f(x)=2sin(x-兀/6)cosx+2cos2x
=2(sinxcosπ/6-cosxsinπ/6)cosx+2cos2x
=√3sinxcosx-cos²x+2cos2x
=√3/2*sin2x-1/2(1+cos2x)+2cos2x
=√3/2*sin2x+3/2cos2x-1/2
=√3sin(2x+π/3)-1/2
由2kπ-π/2≤2x+π/3≤2kπ+π/2
得kπ-5π/12≤x≤kπ+π/12
增区间 [kπ-5π/12,kπ+π/12],k∈Z