Chapter 11.5, Problem 17E

To determine

To Show: The relation $P_2(\cos \theta )=\frac{1}{4}(3\cos 2\theta +1)$ for $x=\cos \theta$ if the first three Legendre polynomials are $P_0\left(x\right)=1$, $P_1\left(x\right)=x$ and $P_2\left(x\right)=\frac{1}{2}\left(3x^2-1\right)$.