## Precalculus (6th Edition) Blitzer

Please note that the graphs of $y=\cos x +\cos 2x$ (the red graph) and $y=\cos 3x$ (the blue graph) do not coincide. For $x=\frac{\pi }{2}$ we have$$\cos \frac{\pi }{2} + \cos 2(\frac{\pi }{2})=-1 \neq 0 = \cos \frac{3\pi }{2}.$$