已知函数f(x)=√3cos2x-2sin²(π/4+x)+1,x∈[π/6,π/2].(1)求f(x)的最大值,并求当f(x)取得最大值时x的值(2)求f(x)单调递增区间.
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![已知函数f(x)=√3cos2x-2sin²(π/4+x)+1,x∈[π/6,π/2].(1)求f(x)的最大值,并求当f(x)取得最大值时x的值(2)求f(x)单调递增区间.](/uploads/image/z/3935807-71-7.jpg?t=%E5%B7%B2%E7%9F%A5%E5%87%BD%E6%95%B0f%28x%29%3D%E2%88%9A3cos2x-2sin%26%23178%3B%28%CF%80%2F4%2Bx%29%2B1%2Cx%E2%88%88%5B%CF%80%2F6%2C%CF%80%2F2%5D.%281%29%E6%B1%82f%28x%29%E7%9A%84%E6%9C%80%E5%A4%A7%E5%80%BC%2C%E5%B9%B6%E6%B1%82%E5%BD%93f%28x%29%E5%8F%96%E5%BE%97%E6%9C%80%E5%A4%A7%E5%80%BC%E6%97%B6x%E7%9A%84%E5%80%BC%EF%BC%882%EF%BC%89%E6%B1%82f%28x%29%E5%8D%95%E8%B0%83%E9%80%92%E5%A2%9E%E5%8C%BA%E9%97%B4.)
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