sin(2x+π/3)=sin2xcos60+sin60cos2x
sin(2x-π/3)=sin2xcos60-sin60cos2x
2(cosx)^2=2×[(1+cos2x)/2]=cos2x+1
f(x)=2sin2xcos60+cos2x+1
f(x)=sin2x+cos2x+1
sin2x＋cos2x
=√2(√2/2sin2x+√2/2cos2x)
=√2(sin2xcos45+cos2xsin45)
=√2sin(2x+45)
f(x)=√2sin(2x+45)+1
( 1 )最小正周期T=2π / w=π
( 2 )单调减区间
f(x)=sinx 单调减区间：(2kπ+π/2,2kπ+3π/2),k∈Z
f(x)=√2sin(2x+45) +1
单调减区间：2kπ+π/2≤ 2x+π/2 ≤2kπ+3π/2
x∈[kπ,kπ+π/2]
( 3 )g(x)=√2sin(2x+45)+1-m
f(x)=√2sin(2x+45)+1
当x=-π/4,f(x)=0
当x=π/4,f(x)=2
当x∈（-π/4,π/4）时
f(x)有最大值√2+1
若无零点
m＜0或m＞1+√2
你题应该是f(x)=sin(2x+π/3)+sin(2x-π/3)+2cosx平方-1
如果你没打错,我写的一定对