Precalculus (6th Edition) Blitzer

We know that the equation is already in the form of an isolated trigonometric function on one side and a constant form on another side. Therefore, the value of $x$ can easily be found by using $\cos \pi =-1$ \begin{align} & \cos \left( x-\frac{\pi }{3} \right)=\cos \pi \\ & x-\frac{\pi }{3}=\pi \\ & x=\pi +\frac{\pi }{3} \\ & x=\frac{4\pi }{3} \end{align} Thus, the equation can be simply solved by using the trigonometric identity. So, there is a need to apply the difference formula of $\cos$.