y=cos^2 x+1/2sin2x =1/2cos2x+1/2sin2x =1/2*根号2*cos(45°+2x)而,y=cosx 的单调性为(0°,90°)单调递减由此,可知: 0°+360°≤45°+2x≤90°+360°于是解出x范围!
y=cos^2 x+1/2sin2x =1/2cos2x+1/2+1/2sin2x =√2/2*sin(45°+2x)+1/2而sin(45°+2x)的范围是(-1.1)可得值域:(1/2-√2/2, 1/2+√2/2)