f(x)=2sinx*cosx-2√3cos^x+√3+b求单调递减区间若f(x)最大值是√3,求实数b的值?

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f(x)=2sinx*cosx-2√3cos^x+√3+b求单调递减区间若f(x)最大值是√3,求实数b的值?
f(x)=2sinx*cosx-2√3cos^x+√3+b求单调递减区间
若f(x)最大值是√3,求实数b的值?

f(x)=2sinx*cosx-2√3cos^x+√3+b求单调递减区间若f(x)最大值是√3,求实数b的值?
f(x)=sin2x-√3cos2x+b
=2(sin2xcosπ/3-cos2xsinπ/3)+b
=2sin(2x-π/3)+b
=2sin[2(x-π/6)]+b
2kπ+π/2≤2(x-π/6)≤2kπ+3π/2
kπ+5/12≤x≤kπ+11π/12,减区间[kπ+5/12,kπ+11π/12]
b=√3-2