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  4. cosec-1((3/2))+cos-1((2/3)) -2 cot-1 ((1/7)) - cot-1(7) is equal to

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Q. $cosec^{-1}\left(\frac{3}{2}\right)+cos^{-1}\left(\frac{2}{3}\right) -2\,cot^{-1} \left(\frac{1}{7}\right) - cot^{-1}\left(7\right)$ is equal to

Inverse Trigonometric Functions

Solution:

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