Question

Prove that the function f(x)= cosx-cos3x is periodc

Answer 1

$f(x+2\pi)=cos(x+2\pi)+cos3(x+2\pi)=cos(x+2\pi)+cos(3x+6\pi)=$

$=cosx+cos3x=f(x).$

Thus, f(x) is periodic with period $2\pi.$