已知函数f(x)=sin(x-π/3)+根号3cos(x-π/3)求函数y=f(x)-1的单调递增区间,设函数g(x)=(1+sinx)f(X).求g(x)的值域

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已知函数f(x)=sin(x-π/3)+根号3cos(x-π/3)求函数y=f(x)-1的单调递增区间,设函数g(x)=(1+sinx)f(X).求g(x)的值域

已知函数f(x)=sin(x-π/3)+根号3cos(x-π/3)求函数y=f(x)-1的单调递增区间,设函数g(x)=(1+sinx)f(X).求g(x)的值域
已知函数f(x)=sin(x-π/3)+根号3cos(x-π/3)
求函数y=f(x)-1的单调递增区间,设函数g(x)=(1+sinx)f(X).求g(x)的值域

已知函数f(x)=sin(x-π/3)+根号3cos(x-π/3)求函数y=f(x)-1的单调递增区间,设函数g(x)=(1+sinx)f(X).求g(x)的值域
f(x)=sin(x-π/3)+√3cos(x-π/3)
=2[1/2*sin(x-π/3)+√3/2*cos(x-π/3)]
=2*[cosπ/3*sin(x-π/3)+sinπ/3*cos(x-π/3)]
=2sin(x-π/3+π/3)
=2sinx
y=f(x)-1=2sinx-1
增区间是[-π/2+2kπ,π/2+2kπ],k∈Z
g(x)=(sinx+1)*2sinx
=2sin²x+2sinx
=2(sin²x+sinx+1/4)-1/2
=2(sinx+1/2)²-1/2
最小值=-1/2
最大值=2*(1+1/2)²-1/2=4
∴值域是[-1/2,4]

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