Embibe Experts Solutions for Chapter: Inverse Trigonometric Functions, Exercise 1: EXERCISE-1

The number $k$ is such that $\tan \left\{\mathrm{arc} \tan \left(2\right)+\mathrm{arc} \tan \left(20k\right)\right\}=k$. The sum of all possible values of $k$ is -

If ${\sin }^{-1}x+{\cot }^{-1}\left(\frac{1}{2}\right)=\frac{\pi }{2}$, then $x$ is -

If $\tan \left({\cos }^{-1}x\right)=\sin \left({\cot }^{-1}\frac{1}{2}\right)$, then $x$ is equal to -

${\sin }^{-1}\left(2x\sqrt{1-x^2}\right)=2{\sin }^{-1}x$ is true if -

Domain of the explicit form of the function $y$ represented implicitly by the equation $\left(1+x\right)\cos y-x^2=0$ is -

If ${\cos }^{-1}x+{\cos }^{-1}y+{\cos }^{-1}z=\pi$, then -

The solution of the inequality ${\left({\tan }^{-1}x\right)}^2-3{\tan }^{-1}x+2\ge 0$ is -

The set of values of $x$, satisfying the equation ${\tan }^2\left({\sin }^{-1}x\right)>1$ is -