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If $\cos(\tan^{-1}x+\cot^{-1}\sqrt 3)=0,$then the value of $x$ is _______________.

$\begin{array}{1 1} \sqrt 3 \\ - \sqrt 3 \\ -\frac{1}{3} \\ \frac{1}{\sqrt 3 } \end{array} $

Can you answer this question?
 
 

1 Answer

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Toolbox:
  • \( tan^{-1}x+cot^{-1}x=\large\frac{\pi}{2} \)
  • \( cos \large\frac{\pi}{2} = 0\:\:\:or\:cos^{-1}0=\large\frac{\pi}{2}\)
Ans:\( \sqrt 3\)
 
The given equation can be written as
\(tan^{-1}x+cot^{-1}\sqrt3=cos^{-1}0\)
 
But \(cos^{-1}0=\large\frac{\pi}{2}\)
\(\Rightarrow\:tan^{-1}x+cot^{-1}\sqrt3=\large\frac{\pi}{2}\)
 
From the above formula we can say that
\(\Rightarrow\: x = \sqrt 3\)

 

answered Feb 18, 2013 by thanvigandhi_1
edited Mar 16, 2013 by thanvigandhi_1
 
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