Embibe Experts Solutions for Chapter: Inverse Trigonometric Functions, Exercise 1: Gujarat Board-2018

Range of $\left[{\cos }^{-1}x\right]$ is (where $\left[\right]=$greatest integer part)

If $0<x<1$ and if ${\tan }^{-1}\left(1-x\right), {\tan }^{-1}\left(x\right)$ and ${\tan }^{-1}\left(1+x\right)$ are in arithmetic progression then $x^3=$

Prove that $\tan \left(\frac{\mathrm{\pi }}{4}+\frac{1}{2}{\cos }^{-1}\frac{a}{b}\right)+\tan \left(\frac{\mathrm{\pi }}{4}-\frac{1}{2}{\cos }^{-1}\frac{a}{b}\right)=\frac{2b}{a}$.

$\sum _{i=0}^2{\cot }^{-1}\{-(i+1\left)\right\}=$

Which of the following is a graph of $f\left(x\right)={\tan }^{-1}x,(x\in R)$?

The value of ${\sec }^{-1}x+{cosec}^{-1}x+{\cos }^{-1}\left(x^{-1}\right)+{\sin }^{-1}\left(x^{-1}\right)$ is (where $\left|x\right|\ge 1,x\in R$)

$\cot \left\{\frac{2019\pi }{2}-\left({cosec}^{-1}\left(\frac{5}{3}\right)+{\tan }^{-1}\left(\frac{2}{3}\right)\right)\right\}=$

Find the value of the $\tan \frac{1}{2}\left\{{\sin }^{-1}\left(\frac{2x}{1+x^2}\right)+{\cos }^{-1}\left(\frac{1-y^2}{1+y^2}\right)\right\},\left|x\right|<1,y>0\text{ and }xy<1,x\ne y$.