If $\sin\left(P\right)=\frac16$ and $\cos\left(P\right)=\frac{\sqrt{35}}{6}$, find $\cot\left(P\right)$ using trigonometric identities.

Is the following trigonometric equation an identity?

$\cot\left(2x\right)=\frac{\cot^2x-1}{2\cot x}$