(2 ^ -1 1 5 + ^ -1 5 2 +2 ^ -1 1 8 ) is equal to. - Vidyadip

MCQ

$\tan \left(2 \tan ^{-1} \frac{1}{5}+\sec ^{-1} \frac{\sqrt{5}}{2}+2 \tan ^{-1} \frac{1}{8}\right)$ is equal to.

A
$1$
✓
$2$
C
$\frac{1}{4}$
D
$\frac{5}{4}$

✓

Answer

Correct option: B.

$2$

b
$\tan \left(2\left(\tan ^{-1} \frac{1}{5}+\tan ^{-1} \frac{1}{8}\right)+\tan ^{-1}\left(\frac{1}{2}\right)\right)$

$=\tan \left[2 \tan ^{-1}\left(\frac{1}{3}\right)+\tan ^{-1}\left(\frac{1}{2}\right)\right]$

$=2$

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