Answer
$$\cot x=\pm\sqrt{\csc^2 x-1}$$
Work Step by Step
Pythagorean Identities:
$$\cot^2 x+1=\csc^2 x$$
Therefore,
$$\cot^2 x=\csc^2 x-1$$
We now take the square root of both sides to get $\cot x$
$$\sqrt{\cot^2 x}=\sqrt{\csc^2 x-1}$$
$$\cot x=\pm\sqrt{\csc^2 x-1}$$
(Do not forget the $\pm$ sign, as $\cot x$ might be positive or negative)
