An important trigonometric function is sin(2x):
[tex]\sin (2x)=2\cdot\sin x\cdot\cos x[/tex]Let's use it to solve the given equation.
[tex]\begin{gathered} 6\cdot\sin (2x)=6\cos x \\ 6\cdot2\cdot\sin x\cdot\cos x=6\cos x \\ \sin x=\frac{6\cdot\cos x}{2\cdot6\cdot\cos x} \\ \sin x=\frac{1}{2} \\ x=\sin ^{-1}(\frac{1}{2}) \\ x=\frac{\pi}{6} \end{gathered}[/tex]