Provide an Appropriate Response $\tan \theta + 1 = \sec \theta$

Short Answer

Provide an appropriate response.
-A student claims that the equation $\tan \theta + 1 = \sec \theta$ is an identity, since by letting $\theta = 0 ^ { \circ }$ we get $0 + 1 = 1$ , a true statement. Comment on this student's reasoning.