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?