If ^ - 1 x + ^ - 1 3 = 2 , then x = - Vidyadip

Question

If ${\cot ^{ - 1}}x + {\tan ^{ - 1}}3 = \frac{\pi }{2}$, then $x =$

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Answer

c
(c) We have ${\cot ^{ - 1}}x + {\tan ^{ - 1}}3 = \frac{\pi }{2}$

$ \Rightarrow \,\,{\cot ^{ - 1}}x + {\tan ^{ - 1}}3 = \frac{\pi }{2}\,\, $

$\Rightarrow \,\,{\tan ^{ - 1}}\frac{1}{x} + {\tan ^{ - 1}}3 = \frac{\pi }{2}$

$ \Rightarrow \,\,{\tan ^{ - 1}}\left( {\frac{{\frac{1}{x} + 3}}{{1 - \frac{1}{x}.3}}} \right) = {\tan ^{ - 1}}\left( {\frac{1}{0}} \right)$

$ \Rightarrow \,\,\frac{{3x + 1}}{{x - 3}} = \frac{1}{0}\,\, \Rightarrow \,\,x = 3$

Aliter : As we know that, ${\tan ^{ - 1}}x + {\cot ^{ - 1}}x = \frac{\pi }{2},$

therefore for the given question, $ x$ should be $3.$

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