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  4. cosec [2 cot -1(5)+ cos -1((4/5))] is equal to:

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Q. $cosec \left[2 \cot ^{-1}(5)+\cos ^{-1}\left(\frac{4}{5}\right)\right]$ is equal to:

JEE MainJEE Main 2021Inverse Trigonometric Functions

Solution:

$cosec\left[2 \tan ^{-1}\left(\frac{1}{5}\right)+\tan ^{-1}\left(\frac{3}{4}\right)\right]$
$cosec\left[\tan ^{-1}\left(\frac{5}{12}\right)+\tan ^{-1}\left(\frac{3}{4}\right)\right]$
$=cosec\left[\tan ^{-1}\left(\frac{56}{33}\right)\right]=\frac{65}{56}$