Let $f\left(x\right)={\cot }^{-1}x+{cosec}^{-1}x$. Then, $f\left(x\right)$ is real for

Important Questions on Inverse Trigonometric Functions

EASY

JEE Advanced

IMPORTANT

Complete Study Pack for Engineering Entrances Objective Mathematics Vol 2>Chapter 4 - Inverse Trigonometric Functions>Target Exercises>Q 62

${\sec }^{-1}\left(\sin x\right)$ is real, if

EASY

JEE Advanced

IMPORTANT

Complete Study Pack for Engineering Entrances Objective Mathematics Vol 2>Chapter 4 - Inverse Trigonometric Functions>Target Exercises>Q 63

If ${\tan }^{-1}\frac{x}{\pi }<\frac{\pi }{3}, x\in N$, then the maximum value of $x$ is

EASY

JEE Advanced

IMPORTANT

Complete Study Pack for Engineering Entrances Objective Mathematics Vol 2>Chapter 4 - Inverse Trigonometric Functions>Target Exercises>Q 64

The solution set of the equation ${\tan }^{-1}x-{\cot }^{-1}x={\cos }^{-1}\left(2-x\right)$ is

HARD

JEE Advanced

IMPORTANT

Complete Study Pack for Engineering Entrances Objective Mathematics Vol 2>Chapter 4 - Inverse Trigonometric Functions>Target Exercises>Q 65

The number of the real solution of  $\sqrt{1+\cos 2x}=\sqrt{2}{\sin }^{-1}\left(\sin x\right), -\pi \le x\le \pi$ is

MEDIUM

JEE Advanced

IMPORTANT

Complete Study Pack for Engineering Entrances Objective Mathematics Vol 2>Chapter 4 - Inverse Trigonometric Functions>Target Exercises>Q 66

The number of real solutions of the equation ${\tan }^{-1}\sqrt{x(x+1)}+{\sin }^{-1}\sqrt{x^2+x+1}=\frac{\pi }{2}$ is

HARD

JEE Advanced

IMPORTANT

Complete Study Pack for Engineering Entrances Objective Mathematics Vol 2>Chapter 4 - Inverse Trigonometric Functions>Target Exercises>Q 67

The number of real solutions $\left(x,y\right)$ where $\left|y\right|=\sin x, y={\cos }^{-1}\left(\cos x\right), -2\pi \le x\le 2\pi$, is

MEDIUM

JEE Advanced

IMPORTANT

Complete Study Pack for Engineering Entrances Objective Mathematics Vol 2>Chapter 4 - Inverse Trigonometric Functions>Target Exercises>Q 68

The set of values of $k$ for which $x^2-kx+{\sin }^{-1}\left(\sin 4\right)>0$ for all real $x$, is

HARD

JEE Advanced

IMPORTANT

Complete Study Pack for Engineering Entrances Objective Mathematics Vol 2>Chapter 4 - Inverse Trigonometric Functions>Target Exercises>Q 69

The sum of the infinite series ${\cot }^{-1}\left(2\right)+{\cot }^{-1}8+{\cot }^{-1}18+{\cot }^{-1}32+\dots$ is