令 t =1-cos x,
则 cos x =1 -t.
所以 (sin x)^2 =1 -(cos x)^2
=1 -(1-t)^2
= -t^2 +2t.
所以 f(t) = -t^2 +2t.
又因为 -1 ≤cos x ≤1,
所以 0 ≤t ≤2.
所以 f(t) = -t^2 +2t,0 ≤t ≤2.
= = = = = = = = =
换元法.