y=1/2(cosx)^2+sinxcosx+3/2(sinx)^2 求周期,最大值和最大值时X的值,求单调增区间

y=1/2cosx^2+sinxcosx+3/2sinx^2
=1/2(1+2sinxcosx+2sinx^2)
=1/2(1+sin2x+1-cos2x)
=1+√2/2sin(2x-π/4)
周期T=π ,x=3/8π,有最大值1+√2/2
单调递增区间[kπ-π/8,kπ+3/8π](K∈Z)

y=1+(2^1/2)/2*sin(2x-π/4)
周期π，当x=π/8时，有最大值1+(2^1/2)/2，kπ+π/8~kπ+5π/8为单调递增，kπ-3π/8~kπ+π/8为单调递减，k为整数。