y=sin2x+2sin方x的最大值和x的集合

y = sin(2x) + 2sin²x
= sin(2x) + 1 - cos(2x)
= 1 + √2[sin(2x)*(√2/2) + cos(2x)*(√2/2)]
= 1 + √2[sin(2x)cos(π/4) + cos(2x)sin(π/4)]
= 1 +√2sin(2x + π/4)
y最大,2x + π/4 = π/2 + 2kπ (k为整数)
x = π/8 + kπ (k为整数)