f(X)=cos2x+2sinx
= 2cos^2 x -1 + 2sinx
= 1- 2sin^2 x + 2sinx
= -2(sinx - 1/2)^2 + 3/2
最小值为 -2(-1-1/2)^2 + 3/2 = -3
最大值为 3/2