因为 f(sin x)=sin [ (4n+1) x ] ,所以 f(cos x)=f[ sin (x +pi/2) ]=sin [ (4n+1) (x +pi/2) ]=sin [ (4n+1) x +2n *pi +pi/2]=sin [ (4n+1) x +pi/2 ]=cos [ (4n+1) x ].