已知f(x)=sin(2x+π/3)+sin(2x-π/3)+2cosx平方,x∈R(1)求f(x)的最小正周期(2)求f(x)的单调减区间(3)若函数g(x)=f(x)-m在区间(-π/4,π/4)上没有零点,求m的取值范围
已知f(x)=sin(2x+π/3)+sin(2x-π/3)+2cosx平方,x∈R(1)求f(x)的最小正周期(2)求f(x)的单调减区间(3)若函数g(x)=f(x)-m在区间(-π/4,π/4)上没有零点,求m的取值范围
数学人气:962 ℃时间:2020-03-27 04:26:18
优质解答
sin(2x+π/3)=sin2xcos60+sin60cos2xsin(2x-π/3)=sin2xcos60-sin60cos2x2(cosx)^2=2×[(1+cos2x)/2]=cos2x+1f(x)=2sin2xcos60+cos2x+1f(x)=sin2x+cos2x+1sin2x+cos2x=√2(√2/2sin2x+√2/2cos2x)=√2(sin2xcos45+c...
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