If $f : [−\pi, \pi]$ is continuous and even on $[−\pi, \pi],$ show there exists a polynomial sequence $\{p_n\}$ such that $p_n\circ\cos$ converges uniformly to $f$ in $[−\pi, \pi]$
I was trying to use theorem of Weiestrass aproximation but I don´t know how to do it. As a hint it says consider the function $g : [−1, 1] \to\Bbb R$ define as $g := f \circ\arccos$.
Please, help me.