cosec [2 ^ -1 (5)+ ^ -1 (4 5 ) ] is equal to ..... . - Vidyadip

MCQ

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

A
$\frac{56}{33}$
✓
$\frac{65}{56}$
C
$\frac{65}{33}$
D
$\frac{75}{56}$

✓

Answer

Correct option: B.

$\frac{65}{56}$

b
$\operatorname{cosec}\left[2 \tan ^{-1}\left(\frac{1}{5}\right)+\tan ^{-1}\left(\frac{3}{4}\right)\right]$

$\operatorname{cosec}\left[\tan ^{-1}\left(\frac{5}{12}\right)+\tan ^{-1}\left(\frac{3}{4}\right)\right]$

$=\operatorname{cosec}\left[\tan ^{-1}\left(\frac{56}{33}\right)\right]=\frac{65}{56}$

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