^ -1 3- ^ -1 (-2) is equal to : - Vidyadip

MCQ

$\tan^{-1}\sqrt{3}-\sec^{-1}(-2)$ is equal to :

A
${\pi}$
✓
$-\frac{\pi}{3}$
C
$\frac{\pi}{3}$
D
$\frac{2\pi}{3}$

✓

Answer

Correct option: B.

$-\frac{\pi}{3}$

$\tan^{-1}(\sqrt{3})=\text{x}$
$\sqrt{3}=\tan\text{x}$
$\tan\frac{\pi}{3}=\tan\text{x}$
$\frac{\pi}{3}=\text{x}$
or ${x}=\frac{\pi}{3}$
Similarly $ \sec^{-1}(-2)=\text{y}$
$-2=\sec\text{y}$
$\sec\frac{2\pi}{3}=\sec\text{y}$
$\text{y}=\frac{2\pi}{3}$
Now $ \tan^{-1}\sqrt{3}-\sec^{-1}(-2)=\text{x}-\text{y}$
$=\frac{\pi}{3}-\frac{2\pi}{3}$
$-\frac{\pi}{3}$

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