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CBSE Class 12 Math 2018 Solved Paper

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Question : 1 of 29
Marks: +1, -0
Find the value of tan⁡−13−cot⁡−1(−3)\tan^{-1} \sqrt{3} - \cot^{-1}(-\sqrt{3})
Solution:  
tan⁡−13−cot⁡−1(−3)\tan^{-1} \sqrt{3} - \cot^{-1}(-\sqrt{3})
= tan⁡−13−[π−cot⁡−1(−3)\tan^{-1} \sqrt{3} - [\pi - \cot^{-1}(-\sqrt{3})] (Since cot⁡−1\cot^{-1} (- x) = π - cot⁡−1\cot^{-1} (x))
= tan⁡−13−π+cot⁡−1(−3)\tan^{-1} \sqrt{3} - \pi + \cot^{-1}(-\sqrt{3})
tan⁡−13+cot⁡−1(−3)\tan^{-1} \sqrt{3} + \cot^{-1}(-\sqrt{3}) - π
= π2−π\frac{\pi}{2} - \pi (Since tan⁡−1\tan^{-1} (x) + cot⁡−1\cot^{-1} (x) = π2\frac{\pi}{2})
= - π2\frac{\pi}{2}
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