y=2(sin^2)x+2cosx-3的最大值是____. 怎么做的?

正确答案:
y=2(sin^2)x+2cosx-3
=2[1-(cos^2)x]+2cosx-3
=-2(cos^2)x+2cosx-1
=-2[(cos^2)x-cosx]-1
=-2[(cos^2)x-cosx+1/4]-1/2
=-2(cosx-1/2)^2-1/2

(sin^2)x+(cos^2)x=1
所以(sin^2)x=1-(cos^2)x
y=2(sin^2)x+2cosx-3
=2[1-(cos^2)x]+2cosx-3
=2cosx-2(cos^2)x-1
=2cosx-2(cos^2)x-[(sin^2)x+(cos^2)x]
=2cosx-(cos^2)x-(sin^2)x
=2cosx-[(cos^2)x+(sin^2)x]
=2cosx-1
因为cosx的最大值为1
所以当x=0时，cosx=1,有y的最大值＝2×1－1＝1