D.P. GUPTA, Preetima Bajpai and, Sanjeev Kumar Jha Solutions for Chapter: Inverse Trigonometric Functions, Exercise 2: Exercise 2

The value of ${\sin }^{-1}\left(\frac{1}{\sqrt{5}}\right)+{\cot }^{-1}\left(3\right)$ is

Find the value of $x$ and $y$ 

${\sin }^{-1}x+{\sin }^{-1}y=\frac{2\pi }{3}, {\cos }^{-1}x-{\cos }^{-1}y=\frac{\pi }{3}$

If $\alpha ={\sin }^{-1}\frac{\sqrt{3}}{2}+{\sin }^{-1}\frac{1}{3}$ and $\beta ={\cos }^{-1}\frac{\sqrt{3}}{2}+{\cos }^{-1}\frac{1}{3}$, then 

Find the value of ${\cos }^{-1}\cos \left(\frac{7\pi }{6}\right)$

If ${\sin }^{-1}x+{\sin }^{-1}y=\frac{2\pi }{3}$, then find the value of ${\cos }^{-1}x+{\cos }^{-1}y$

If ${\sin }^{-1}\frac{1}{x}={\sin }^{-1}\frac{1}{a}+{\sin }^{-1}\frac{1}{b}$, then the value of $x$ is

The value of ${\cot }^{-1}\left\{\frac{\sqrt{1-\sin x}+\sqrt{1+\sin x}}{\sqrt{1-\sin x}-\sqrt{1+\sin x}}\right\}$ is $\left(0<x<\frac{\pi }{2}\right)$

If ${\sin }^{-1}x+{\sin }^{-1}y+{\sin }^{-1}z=\frac{3\pi }{2}$, then the value of $x^{100}+y^{100}+z^{100}-\frac{3}{x^{101}+y^{101}+z^{101}}$ is