# Crazy Inverse Mistake

**Algebra**Level 3

Joey has just learnt about inverse trigonometry and is very excited about it. He thinks that what he does will always work out.

So he claims that

\(tan^{-1}(x) \cdot cot^{-1}(x)\) = \(1\), inspired from the identity \(tan(x) \cdot cot(x)\)= \(1\).

How many real values of \(x\) are there such that >\(tan^{-1}(x) \cdot cot^{-1}(x)\) = \(1\)