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Inverse Trigonometric Functions — Maths STD 12 Science — Question

Gujarat BoardEnglish MediumSTD 12 ScienceMathsInverse Trigonometric Functions1 Mark
Question
$\tan ^{-1} \sqrt{3}-\cot ^{-1}(-\sqrt{3})$  is equal to
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Answer

$\tan ^{-1}(\sqrt{3})-\cot ^{-1}(-\sqrt{3})$ 
 = $\tan ^{-1} \sqrt{3}-\left(\pi-\cot ^{-1} \sqrt{3}\right)$ 
 = $\tan ^{-1} \sqrt{3}+\cot ^{-1} \sqrt{3}-\pi$ 
 = $\frac{\pi}{2}-\pi$ 
 = $-\frac{\pi}{2}$

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