How do you evaluate sec [Cot^-1 (-6)]?

Dec 28, 2016

$- \frac{\sqrt{37}}{6}$

Explanation:

$\sec \left[{\cot}^{- 1} \left(- 6\right)\right]$

$\frac{1}{\cos \left[{\cot}^{-} 1 \left(- 6\right)\right]}$

Using the following rule , we can simplify the denominator:

$\frac{1}{\left(\frac{- 6}{\sqrt{1 + {\left(- 6\right)}^{2}}}\right)}$

$\frac{\sqrt{1 + 36}}{- 6}$

$- \frac{\sqrt{37}}{6}$