(1)f(COSX)=COS17x 求证F(SINX)=17X(2)已知X属于R,N属于Z且F(SINX)=SIN(4N+1)求F(COSX)

问题描述:

(1)f(COSX)=COS17x 求证F(SINX)=17X
(2)已知X属于R,N属于Z且F(SINX)=SIN(4N+1)求F(COSX)

(1)sinx=cos(π/2-x)所以f(sinx)=f[cos(π/2-x)]=cos[17(π/2-x)]=cos(17π/2-17x)=cos(π/2-17x)=sin17x (2)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-(...