一道高等数学关于复合函数的题;f (sin x/2)=1+cosx ,则f (cos x/2)=?？

Question

如题所述

Answer 1

f (sin x/2)=1+cosx
=1+(1-2sin x/2)
=-2sin x/2+2
所以
f (cos x/2)=－2cos x/2＋2,2,f(sin x/2)
=1+cosx
=(cos x/2)^2+(sin x/2)^2+(cos x/2)^2-(sin x/2)^2
=2*(cos x/2)^2
=2*(1-(sin x/2)^2)
换元,令 t=sin x/2
则f(t)=2*(1-t^2)
再令t=cos x/2
则f(cos x/2)
=2*(1-(cos x/2)^2)
=2*(sin x/2)^2
=1-cos x,1,一道高等数学关于复合函数的题;f (sin x/2)=1+cosx ,则f (cos x/2)=?
f (sin x/2)=1+cosx ,则f (cos x/2)=?