Chapter 13, Problem 17PS

To determine

To prove: The function $u\left(x,t\right)=\frac{1}{2}\left[\sin \left(x-t\right)+\sin \left(x+t\right)\right]$ is a solution to one-dimensional wave equation, $\frac{{\partial }^{2}u}{\partial t^2}=\frac{{\partial }^{2}u}{\partial x^2}$.