# 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 >$$tan^{-1}(x) \cdot cot^{-1}(x)$$ = $$1$$

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