INVERSE TRIGNOMETRIC FUNCTIONS — Maths STD 12 Science — Question

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

$\tan^{-1}(\sqrt{3})=\text{x}$

$\sqrt{3}=\tan\text{x}$

$\tan\frac{\pi}{3}=\tan\text{x}$

$\frac{\pi}{3}=\text{x}$

$\text{or x}=\frac{\pi}{3}$

$\text{Similarly}\ \sec^{-1}(-2)=\text{y}$

$-2=\sec\text{y}$

$\sec\frac{2\pi}{3}=\sec\text{y}$

$\text{y}=\frac{2\pi}{3}$

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

$=\frac{\pi}{3}-\frac{2\pi}{3}$

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