G Tewani Solutions for Chapter: Inverse Trigonometric Functions, Exercise 2: DPP

If maximum and minimum values of $\left|{\sin }^{-1}x\right|+\left|{\cos }^{-1}x\right|$ are $M$ and $m,$ then $M+m$ is

If the function $f\left(x\right)={\sin }^{-1}x+{\cos }^{-1}x$ and $g\left(x\right)$ are identical, then $g\left(x\right)$ can be equal to

The value of $x$ satisfying ${\sin }^{-1}\left(\sqrt{\frac{3x-1}{25}}\right)+{\sin }^{-1}\left(\sqrt{\frac{3x+1}{25}}\right)=\frac{\pi }{2}$ lies in the interval

The set of values $k$ for which the equation ${\sin }^{-1}x+{\cos }^{-1}x+\pi \left(\right|x|-2)=k\pi$ possesses real solution is $[a, b]$, then the value of $a+b$ is

The solution set of the inequality $\left(\sin x+{\cos }^{-1}x\right)-\left(\cos x-{\sin }^{-1}x\right)\ge \frac{\pi }{2}$ is equal to

The number of integral values in the range of the function $f\left(x\right)={\sin }^{-1}x-{\cot }^{-1}x+x^2+2x+6$ is

If ${\sin }^{-1}\left(\frac{\sqrt{x}}{2}\right)+{\sin }^{-1}\left(\sqrt{1-\frac{x}{4}}\right)+{\tan }^{-1}y=\frac{2\pi }{3}$, then

${\cos }^{-1}\left(\sqrt{\frac{a-x}{a-b}}\right)={\sin }^{-1}\left(\sqrt{\frac{x-b}{a-b}}\right)$ is possible if