The general solution of cosx cos 6x= - 1 is

$\begin{array}{l}\cos \mathrm{xcos}6\mathrm{x}=-1\\ \text{ or }2\cos \mathrm{xcos}6\mathrm{x}=-2\\ \text{ or }\cos 7\mathrm{x}+\cos 5\mathrm{x}=-2\\ \text{ or }\cos 7\mathrm{x}=-1\text{ and }\cos 5\mathrm{x}=-1\end{array}$

The value of x satisfying these two equations simultaneously and lying between 0 and $2\mathrm{\pi }$ is$\mathrm{\pi }$. 

Therefore, the general solution is $\mathrm{x}=2\mathrm{n\pi }+\mathrm{\pi },\mathrm{n}\in \mathrm{Z}$

thus, $\mathrm{x}=(2\mathrm{n}+1)\mathrm{\pi },\mathrm{n}\in \mathrm{Z}$