已知x∈R ,n∈Z,且f(sinx)=sin(4n+1)x,则f(cosx)=

问题描述:

已知x∈R ,n∈Z,且f(sinx)=sin(4n+1)x,则f(cosx)=

f(cosx)
=f[sin(π/2-x)]
=sin(4n+1)(π/2-x)
=sin[(4n+1)π/2-(4n+1)x]
=sin[2nπ+π/2-(4n+1)x]
=sin[π/2-(4n+1)x]
=cos(4n+1)x