Chapter 5 - Section 5.3 - Double-Angle, Power-Reducing, and Half-Angle Formulas - Exercise Set - Page 682: 98

The graphs do not appear to coincide.

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