已知函数f(x)=√3cos2x+2sin(x+π/2)cos(x+π/2) (1)将函数表示为正弦型函数 (2)在R内求函数的单调递增区间

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已知函数f(x)=√3cos2x+2sin(x+π/2)cos(x+π/2) (1)将函数表示为正弦型函数 (2)在R内求函数的单调递增区间
已知函数f(x)=√3cos2x+2sin(x+π/2)cos(x+π/2) (1)将函数表示为正弦型函数 (2)在R内求函数的
单调递增区间

已知函数f(x)=√3cos2x+2sin(x+π/2)cos(x+π/2) (1)将函数表示为正弦型函数 (2)在R内求函数的单调递增区间
f(x)=√3cos2x+2sin(x+π/2)cos(x+π/2)
=√3cos2x+sin(2x+π)
=√3cos2x-sin2x
=2(√3/2cos2x-1/2sin2x)
=2(sinπ/3cos2x-cosπ/6sin2x)
=2sin(π/3-2x)
单调递增区间:2kπ-π/2

f(x)=√3cos2x+2sin(x+π/2)cos(x+π/2) =f(x)=√3cos2x+2cosx(-sinx)=f(x)=√3cos2x-sin2x
=2sin(π/3-2x)=-sin(2x-π/3)
单调递增区间满足2kπ+π/2<=2x-π/3<=2kπ+3π/2
即为kπ+5π/12<=x<=kπ+11π/12
{x|kπ+5π/12<=x<=kπ+11π/12,k∈z}