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Find the value of \( tan^{-1} \sqrt 3 - cot^{-1} (-\sqrt 3) \)

\[ \begin{array} (A) \pi \quad & (B) -\frac{\pi}{2} \quad & (C) 0 \quad & (D) 2\sqrt3 \end{array} \]

1 Answer

Toolbox:
  • \(tan^{-1}\sqrt{3}=\large\frac{\pi}{3}\)
  • \(cot^{-1}-\sqrt{3}=\pi-\large\frac{\pi}{6}\)
Ans (B)
since the principal interval of tan is (\(-\large\frac{\pi}{2},\large\frac{\pi}{2})\) and
that of cot is (0,\(\pi\)), \(tan^{-1}\sqrt{3}=\large\frac{\pi}{3}\:\) and \(\:cot^{-1}-\sqrt{3}=\pi-\large\frac{\pi}{6}\)
The given expression becomes \( \large\frac{\pi}{3}- \bigg(\pi- \large\frac{\pi}{6} \bigg) =- \large\frac{\pi}{2}\)
answered Feb 23, 2013 by thanvigandhi_1
edited Jul 9, 2014 by balaji.thirumalai
 

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