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  4. tan[cos-1((1/√82))-sin-1((5/√26))] is equal to

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Q. $tan\left[cos^{-1}\left(\frac{1}{\sqrt{82}}\right)-sin^{-1}\left(\frac{5}{\sqrt{26}}\right)\right]$ is equal to

Inverse Trigonometric Functions

Solution:

$tan\left[cos^{-1}\left(\frac{1}{\sqrt{82}}\right)-sin^{-1}\left(\frac{5}{\sqrt{26}}\right)\right]$
$=tan\left(tan^{-1}9-tan^{-1}5\right)$
$=tan\left\{tan^{-1}\left(\frac{9-5}{1+9\times5}\right)\right\}=\frac{2}{23}$