# How do you evaluate tan(arctan(10))?

Jan 25, 2017

$\tan \left(\arctan \left(10\right)\right) = 10$

#### Explanation:

Because $\arctan \left(x\right) = {\tan}^{- 1} \left(x\right)$, we can see that $\tan \left(x\right)$ and $\arctan \left(x\right)$ are inverses of each other.

Remember that $f \left({f}^{- 1} \left(x\right)\right) = x$

In this case, replace $f$ with $\tan$ and $x$ with $10$.

Then we get

$\tan \left({\tan}^{- 1} \left(10\right)\right) = \tan \left(\arctan \left(10\right)\right) = 10$

Jan 25, 2017

10

#### Explanation:

tan(arctan(10)

$\therefore = \tan \left(84.28940656\right)$

$\therefore = 10$