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

​Find the principal value of the following: ${\mathrm{cosec}}^{-1}\left(-\sqrt{2}\right)$

​Find the principal value of the following: ${\mathrm{cosec}}^{-1}(-2)$

​Find the principal value of the following:${cosec}^{-1}\left(\frac{2}{\sqrt{3}}\right)$

Determine whether ${\mathrm{cosec}}^{-1}\left(\frac{\sqrt{3}}{2}\right)$ is defined or undefined, if defined then find the set of values.

For the principal value, evaluate the following: ${\sin }^{-1}\left(\frac{\sqrt{3}}{2}\right)+ {\mathrm{cosec}}^{-1}\left(-\frac{2}{\sqrt{3}}\right)$

For the principal value, evaluate the following: ${\sec }^{-1}\left(\sqrt{2}\right)+2{cosec}^{-1}(-\sqrt{2})$

For the principal value, evaluate the following: ${\sin }^{-1}\left[\cos \left\{2{cosec}^{-1}(-2)\right\}\right]$

For the principal value, evaluate the following: ${\mathrm{cosec}}^{-1}\left(2\tan \left(\frac{11\pi }{6}\right)\right)$.