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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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