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CBSE Class 12 Math 2022 Term I Solved Paper

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Question : 34 of 50
Marks: +1, -0
The principal value of [tan⁡−13−cot⁡−1(−3)][ \tan^{-1} \sqrt{3} - \cot^{-1}(-\sqrt{3}) ] is
Solution:     👈: Video Solution
We have,
tan⁡−13−cot⁡−1  (−3)\tan^{-1} \sqrt{3} - \cot^{-1}\;(-\sqrt{3})
  =  π3−(π−  π6)\;=\;\frac{\pi}{3} - \left( \pi - \;\frac{\pi}{6} \right)
  =tan⁡−1(tan⁡  π3)−π+cot⁡−1cot⁡  π6\;=\tan^{-1} \left( \tan \;\frac{\pi}{3} \right) - \pi + \cot^{-1} \cot \;\frac{\pi}{6}
  =  π3−  5π6\;=\;\frac{\pi}{3} - \;\frac{5\pi}{6}
  =−  π2\;=-\;\frac{\pi}{2}
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