Question

已知f(cosx)=cos17x,求证f(sinx)=sin17x

Answer 1

证:
f(sinx)=f(cos(Pi/2-x))
=cos[17(Pi/2-x)]
=cos(17Pi/2-17x)
=cos[4Pi+(Pi/2-x)]
=cos(Pi/2-17x)
=sin17x.证完.

Answer 2

令cosx=t，所以x=cocost，所以cost=cos17(cocost)。