Explain $\tan^2(\tan^{-1}(x))$ becoming $x^2$ How does $\tan^2(\tan^{-1}(x))$ become $x^2$?

I feel that the answer should contain a tan somewhere and not just simply $x^2$. "Why?" you might ask, well I thought that $\tan^2(\theta)$ was a special function that has to be rewritten a specific way.

Because $\tan^{-1}x $ is not the reciprocal of $\tan x$, but the inverse function $\arctan x$.
