Provide an Appropriate Response $1 + \cot ^ { 2 } \theta = \csc ^ { 2 } \theta$

Short Answer

Provide an appropriate response.
-A student claims: "Since $1 + \cot ^ { 2 } \theta = \csc ^ { 2 } \theta$ , I should be able to also say $1 + \cot \theta = \csc \theta$ if I take the square root of both sides." Comment on the student's statement.