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  4. cot((π/4)-2 cot-1 3) =

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