$Thevalueof\text{\hspace{0.17em}x }whichsatisfie 8^{1+\left|\cos x\right|+{\left|\cos x\right|}^2}+\mathrm{................}=64in[-\pi ,\pi ]is$

$\begin{array}{l}{8^{1+\left|\cos x\right|+{\cos }^{2}x}}^{+\mathrm{................}}=64=8^2\Rightarrow 1+\left|\cos x\right|+{\cos }^{2}x+\mathrm{..........}=2\\ \Rightarrow \frac{1}{1-\left|\cos x\right|}=2\Rightarrow 1-\left|\cos x\right|=\frac{1}{2}\Rightarrow \left|\cos x\right|=\frac{1}{2}\Rightarrow \cos x=\pm \frac{1}{2}\Rightarrow x=\pm \frac{\pi }{3},\pm \frac{2\pi }{3}.\end{array}$