Question

If \[\cos\left( \tan^{- 1} x + \cot^{- 1} \sqrt{3} \right) = 0\] , find the value of x.

 

Answer 1

\[\cos\left( \tan^{- 1} x + \cot^{- 1} \sqrt{3} \right) = 0\]
\[ \Rightarrow \cos\left( \tan^{- 1} x + \cot^{- 1} \sqrt{3} \right) = \cos\left( \frac{\pi}{2} \right)\]
\[ \Rightarrow \tan^{- 1} x + \cot^{- 1} \sqrt{3} = \frac{\pi}{2}\]
\[ \Rightarrow x = \sqrt{3} \left[ \because \tan^{- 1} y + \cot^{- 1} y = \frac{\pi}{2} \right]\]
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