^ -1 ( 1+3 3+3 )+ ^ -1 ( 8+4 3 6+3 3 ) is equal to ......... - Vidyadip

MCQ

$\tan ^{-1}\left(\frac{1+\sqrt{3}}{3+\sqrt{3}}\right)+\sec ^{-1}\left(\sqrt{\frac{8+4 \sqrt{3}}{6+3 \sqrt{3}}}\right)$ is equal to $.........$

A
$\frac{\pi}{4}$
B
$\frac{\pi}{2}$
✓
$\frac{\pi}{3}$
D
$\frac{\pi}{6}$

✓

Answer

Correct option: C.

$\frac{\pi}{3}$

c
$\tan ^{-1}\left(\frac{1+\sqrt{3}}{3+\sqrt{3}}\right)+\sec ^{-1}\left(\sqrt{\frac{8+4 \sqrt{3}}{6+3 \sqrt{3}}}\right)$

$=\tan ^{-1}\left(\frac{1}{\sqrt{3}}\right)+\sec ^{-1}\left(\frac{2}{\sqrt{3}}\right)=\frac{\pi}{3}$

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