Question

Wnte the value of\[\cos\left( \frac{\tan^{- 1} x + \cot^{- 1} x}{3} \right), \text{ when } x = - \frac{1}{\sqrt{3}}\]

Answer 1

\[\cos\left( \frac{\tan^{- 1} x + \cot^{- 1} x}{3} \right) = \cos\left( \frac{\pi}{6} \right) \left[ \because \tan^{- 1} x + \cot^{- 1} x = \frac{\pi}{2} \right]\]
\[ = \frac{\sqrt{3}}{2}\]