Question

已知f（cosx）=cos17x，求证：f（sinx）=sin17x

已知f（cosx）=cos17x，求证：f（sinx）=sin17x．

Answer 1

f（sinx）=f（cos（

π

2

-x））=cos[17（

π

2

-x）]=cos（

17π

2

-17x）=cos[8π+（

π

2

-17x）]=cos（

π

2

-17x）=sin17x．

Answer 2

f(sinx)
=f[cos(π/2-x)]
=cos[17(π/2-x)]
=cos(4×2π+π/2-17x)
=cos(π/2-17x)
=sin17x