${\tan ^{ - 1}}\sqrt 3 - {\cot ^{ - 1}}( - \sqrt 3 )$ is equal to
(A) $\pi$
(B) $- \frac{\pi }{2}$
(C) 0
(D) $2\sqrt 3$
${\tan ^{ - 1}}\sqrt 3 - {\cot ^{ - 1}}( - \sqrt 3 )$ is equal to
(A) $\pi$
(B) $- \frac{\pi }{2}$
(C) 0
(D) $2\sqrt 3$
Official Solution
VVidaara Team
✓ Verified solution
NCERT & Exemplar
Option B is correct
${\tan ^{ - 1}}\sqrt 3 - {\cot ^{ - 1}}( - \sqrt 3 ) = {\tan ^{ - 1}}\sqrt 3 - (\pi - {\cot ^{ - 1}}\sqrt 3 )$
$= {\tan ^{ - 1}}\sqrt 3 - \pi + {\cot ^{ - 1}}\sqrt 3 = \frac{\pi }{3} - \pi + \frac{\pi }{6} = \frac{\pi }{2} - \pi = - \frac{\pi }{2}.$
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