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

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Answer 1 · 2016-12-28T23:21:21

$- \frac{\sqrt{37}}{6}$ $-sqrt37/6$

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

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

Using the following rule , we can simplify the denominator:
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$\frac{1}{(\frac{- 6}{\sqrt{1 + {(- 6)}^{2}}})}$ $1/{(frac{-6}{sqrt(1+(-6)^2)})}$

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

$- \frac{\sqrt{37}}{6}$ $-frac{sqrt37}{6}$

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