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Q. $\cot \left(\frac{\pi}{4}-2 \cot ^{-1} 3\right)=$

Inverse Trigonometric Functions

Solution:

$\cot \left\{\frac{\pi}{4}-2 \cot ^{-1} 3\right\}=\cot \left\{\frac{\pi}{4}-2 \tan ^{-1} \frac{1}{3}\right\}$
$=\cot \left\{\frac{\pi}{4}-\tan ^{-1}\left(\frac{\frac{2}{3}}{1-\frac{1}{9}}\right)\right\}=\cot \left\{\frac{\pi}{4}-\tan ^{-1}\left(\frac{3}{4}\right)\right\}$
$=\frac{1}{\tan \left\{\frac{\pi}{4}-\tan ^{-1}\left(\frac{3}{4}\right)\right\}}=\frac{1+\frac{3}{4}}{1-\frac{3}{4}}=7$