^ -1 (3)- ^ -1 (-2) cosec^ -1 (-2)+ ^ -1 (-1 2 ) = - Vidyadip

MCQ

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

A
$\frac{4}{5}$
B
$-\frac{4}{5}$
C
$\frac{3}{5}$
D
0

✓

Answer

(b) : $
\begin{aligned}
& \frac{\tan ^{-1}(\sqrt{3})-\sec ^{-1}(-2)}{\operatorname{cosec}^{-1}(-\sqrt{2})+\cos ^{-1}\left(\frac{-1}{2}\right)}=\frac{(\pi / 3)-(2 \pi / 3)}{(-\pi / 4)+(2 \pi / 3)} \\
& =\frac{-\pi / 3}{5 \pi / 12}=\frac{-4}{5}
\end{aligned}
$

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