Answer
$$1+\cot^2=\csc^2$$
This statement was wrongly written, since it lacks the argument $(\theta, x, etc. )$ of the function.
Work Step by Step
$$1+\cot^2=\csc^2$$
This statement was wrongly written, since it lacks the argument of the function.
As stated in the Caution part of the text, when dealing with trigonometric expressions and identities, we must include the argument $(\theta, x, etc.)$ of the function. Lacking them would lead to wrong statements.