# 6542: T - Trigonometry - Example 6

The display shows $\color{blue}{y = \sin x}$ in blue and $\color{red}{y = \sin \left( {x + a} \right) + \sin \left( {x - a} \right)}$ in red. Use this display to find the value of $a$ such that $\sin \left( {x + a} \right) + \sin \left( {x - a} \right) = \sin x$ . Can you prove it?