f(x)=cos(2x)+2sin(x)
=1-2sin²x+2sinx
=-2sin²x+2sinx+1
=-2(sinx-1/2)²+3/2
若求值域,则
设t=sinx∈[-1,1]
y=-2(t-1/2)²+3/2
t=1/2时,ymax=3/2
t=-1时,ymin=-3
f(x)值域为[-3,3/2]