The value of $\underset{n\to \infty }{\lim }6\tan \left\{\sum _{r=1}^n{\tan }^{-1}\left(\frac{1}{r^2+3r+3}\right)\right\}$ is equal to

Important Questions on Inverse Trigonometric Functions

MEDIUM

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 13 - Inverse Trigonometric Functions>JEE Main - 29 June 2022 Shift 1>Q 41

$50\tan \left(3{\tan }^{-1}\left(\frac{1}{2}\right)+2{\cos }^{-1}\left(\frac{1}{\sqrt{5}}\right)\right)+$$4\sqrt{2}\tan \left(\frac{1}{2}{\tan }^{-1}\left(2\sqrt{2}\right)\right)$ is equal to ______.

HARD

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 13 - Inverse Trigonometric Functions>JEE Main - 25 July 2022 Shift 2>Q 42

Let $x=\sin \left(2{\tan }^{-1}\alpha \right)$ and $y=\sin \left(\frac{1}{2}{\tan }^{-1}\frac{4}{3}\right)$. If $S=\left\{\alpha \in \mathrm{ℝ}:y^2=1-x\right\}$, then $\sum _{\alpha \in S}16{\alpha }^3$ is equal to _______.

MEDIUM

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 13 - Inverse Trigonometric Functions>JEE Main - 26 July 2022 Shift 1>Q 43

$\tan \left(2{\tan }^{-1}\frac{1}{5}+{\sec }^{-1}\frac{\sqrt{5}}{2}+2{\tan }^{-1}\frac{1}{8}\right)$ is equal to:

MEDIUM

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 13 - Inverse Trigonometric Functions>JEE Main - 26 July 2022 Shift 2>Q 44

If $0<x<\frac{1}{\sqrt{2}}$ and $\frac{{\sin }^{-1}x}{\alpha }=\frac{{\cos }^{-1}x}{\beta }$, then a value of $\sin \left(\frac{2\pi \alpha }{\alpha +\beta }\right)$ is

MEDIUM

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 13 - Inverse Trigonometric Functions>JEE Main - 27 July 2022 Shift 1>Q 45

For $k\in \mathrm{ℝ}$, let the solutions of the equation $\cos \left({\sin }^{-1}\left(x\cot \left({\tan }^{-1}\left(\cos \left({\sin }^{-1}x\right)\right)\right)\right)\right)=k,0<\left|x\right|<\frac{1}{\sqrt{2}}$ be $\alpha$ and $\beta$, where the inverse trigonometric functions take only principal values. If the solutions of the equation $x^2-bx-5=0$ are $\frac{1}{{\alpha }^2}+\frac{1}{{\beta }^2}$ and $\frac{\alpha }{\beta }$, then $\frac{b}{k^2}$ is equal to ______.

MEDIUM

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 13 - Inverse Trigonometric Functions>JEE Main - 28 July 2022 Shift 1>Q 46

Considering only the principal values of the inverse trigonometric functions, the domain of the function $f\left(x\right)={\cos }^{-1}\left(\frac{x^2-4x+2}{x^2+3}\right)$ is

MEDIUM

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 13 - Inverse Trigonometric Functions>JEE Main - 28 July 2022 Shift 1>Q 47

Considering the principal values of the inverse trigonometric functions, the sum of all the solutions of the equation ${\cos }^{-1}\left(x\right)-2{\sin }^{-1}\left(x\right)={\cos }^{-1}\left(2x\right)$ is equal to

MEDIUM

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 13 - Inverse Trigonometric Functions>JEE Main - 29 July 2022 Shift 2>Q 48

The domain of the function $f\left(x\right)={\sin }^{-1}\left(\frac{x^2-3x+2}{x^2+2x+7}\right)$ is