G Tewani Solutions for Chapter: Inverse Trigonometric Functions, Exercise 1: DPP

The complete set of values of $a$ for which the function $f\left(x\right)={\tan }^{-1}\left(x^2-18x+a\right)>0; \forall x\in R$

The value of ${\cos }^{-1}\left(-\sin \frac{7\mathrm{\pi }}{6}\right)$ is

The value of $\sec \left[{\sin }^{-1}\left(-\sin \frac{50\mathrm{\pi }}{9}\right)+{\cos }^{-1}\left(\cos \left(-\frac{31\mathrm{\pi }}{9}\right)\right)\right]$ is equal to

The maximum value of the function $f\left(x\right)={\left({\sin }^{-1}\left(\sin x\right)\right)}^2-{\sin }^{-1}\left(\sin x\right)$

The solution of the equation ${\sin }^{-1}\left|\sin x\right|=\sqrt{{\sin }^{-1}\left|\sin x\right|}$ is

The value of $\sin \left(\frac{1}{4}{\sin }^{-1}\frac{\sqrt{63}}{8}\right)$ is

Let $f\left(x\right)={\cos }^{-1}\left(\frac{1-{\tan }^2\frac{x}{2}}{1+{\tan }^2\frac{x}{2}}\right)$, then which of the following statement is/are true?

If $f\left(x\right)={\sin }^{-1}\left(\sin x\right), g\left(x\right)={\cos }^{-1}\left(\cos x\right)$ and $h\left(x\right)={\cot }^{-1}\left(\cot x\right),$ then which of the following is/are correct?