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Home  >>  CBSE XII  >>  Math  >>  Model Papers
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Solve the following for x \[ tan^{-1}x+2cot^{-1}x=\frac{2\pi}{3} \]

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  • \(tan^{-1}x+cot^{-1}x=\frac{\pi}{2}\)
  • \(cot\frac{\pi}{6}=\sqrt3\)
Given equation can be written as
\(\large\:tan^{-1}x+cot^{-1}x+cot^{-1}x=\large\frac{2\pi}{3}\)
We know that \(tan^{-1}x+cot^{-1}x=\frac{\pi}{2}\)
\(\Rightarrow\:\large\frac{\pi}{2}+cot^{-1}x=\large\frac{2\pi}{3}\)
\(\Rightarrow\:\large\:cot^{-1}x=\large\frac{2\pi}{3}-\large\frac{\pi}{2}=\large\frac{\pi}{6}\)
\(\Rightarrow\:\large\:x=\large\:cot\frac{\pi}{6}=\large\sqrt3\)
answered Mar 22, 2013 by rvidyagovindarajan_1
 

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