R D Sharma Solutions for Chapter: Inverse Trigonometric Functions, Exercise 1: EXERCISE

 Find the domain of $f\left(x\right)=2{\cos }^{-1}2x+{\sin }^{-1}x$

 Find the domain of $f\left(x\right)={\cos }^{-1}x+\cos x$

Find the principal value of each of the following:

${\cos }^{-1}\left(-\frac{\sqrt{3}}{2}\right)$

Find the principal value of each of the following: ${\cos }^{-1}\left(-\frac{1}{\sqrt{2}}\right)$

Find the principal value of each of the following:

${\cos }^{-1}\left(\sin \frac{4\pi }{3}\right)$

Find the principal value of each of the following: ${\cos }^{-1}\left(\tan \frac{3\pi }{4}\right)$

Find principal value: ${\cos }^{-1}\left(\frac{1}{2}\right)-2{\sin }^{-1}\left(-\frac{1}{2}\right)$