# How do you evaluate \sec[\cot^{-1}(-6)] ?

How do you evaluate $\mathrm{sec}\left[{\mathrm{cot}}^{-1}\left(-6\right)\right]$ ?
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Explanation
$\mathrm{sec}\left[{\mathrm{cot}}^{-1}\left(-6\right)\right]$
$=\frac{1}{{\mathrm{cos}}^{-1}\left(-6\right)}$
Using the following rule , we can simplify the denominator:
$=\frac{1}{\left(\frac{-6}{\sqrt{1+{\left(-6\right)}^{2}}}\right)}$
$=\frac{\sqrt{1+36}}{-6}$
$=-\frac{\sqrt{37}}{6}$