Write \(cot^{-1}(\frac{1}{\sqrt{x^2-1}})\), \(x > 1\) in the simplest form.
Solution
Let \(x = sec\theta\), then \(\sqrt{x^2-1} = \sqrt{sec^2\theta-1} =
tan\theta\). Therefore, \(cot^{-1}(\frac{1}{\sqrt{x^2-1}}) =
cot^{-1}(cot\theta) = \theta = sec^{-1}x\), which is the simplest
form.
