[tex]\bf cos\left( x+\frac{\pi }{3} \right)+cos\left( x-\frac{\pi }{3} \right)=1\\\\
-----------------------------\\\\\
[cos(x)cos\left( \frac{\pi }{3} \right)\underline{-sin(x)sin\left( \frac{\pi }{3} \right)}]
+ [cos(x)cos\left( \frac{\pi }{3} \right)\underline{+sin(x)sin\left( \frac{\pi }{3} \right)}]=1
\\\\\\[/tex]
[tex]\bf cos(x)cos\left( \frac{\pi }{3} \right)+cos(x)cos\left( \frac{\pi }{3} \right)=1\implies 2cos(x)cos\left( \frac{\pi }{3} \right)=1
\\\\\\
2cos(x)\cdot \cfrac{1}{2}=1\implies cos(x)=1\implies \measuredangle x=cos^{-1}(1)
\\\\\\
\measuredangle x =
\begin{cases}
0\\
2\pi
\end{cases}[/tex]
