y=2cosxsin(x+π/3)-√3sin^2 x+sinxcosx
=2cosx(1/2sinx+√3/2cosx)-√3(1-cosxcosx)+sinxcosx
=2sinxcosx+2√3cosxcosx)-√3
=sin2x+√3(1+cos2x)基败困-√3
=2(1/搏念2sin2x+√3/2cos2x)
=2sin(2x+π/3)
所以最小正周期:2π/2=π
2、函数y=sin(π/3-2x)+cos2x的周期为:π
函数y=2(cos^2)x+1的周期为 π
y=cos2x+2
3、y=2sin(π/6-2x)(x属于[0,π]为增函数的区间枯罩是x∈〔π/3,5π/6〕
x∈〔0,π/3〕时,y从1/2到-1为单调递减区间
x∈〔π/3,5π/6〕,y从-1到1为单调递增区间
x∈〔5π/6,π〕,y从1到1/2为单调递减区间
懒鬼!