Number of solutions of $4{\cos }^{-1}\left(\cos \left|x\right|\right)=\left|x\right|$ is equal to

Important Questions on Inverse Trigonometric Functions

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IMPORTANT

Gamma Question Bank for Engineering Mathematics>Chapter 22 - Inverse Trigonometric Functions>Assignment>Q 56

The value of ${\cot }^2\left({\cot }^{-1}3+{\cot }^{-1}7+{\cot }^{-1}13+{\cot }^{-1}21\right)$ is equal to

EASY

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IMPORTANT

Gamma Question Bank for Engineering Mathematics>Chapter 22 - Inverse Trigonometric Functions>Assignment>Q 57

The value of ${\sin }^{-1}\left(\sin 9\right)+{\tan }^{-1}\left(\tan 9\right)$ is equal to

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IMPORTANT

Gamma Question Bank for Engineering Mathematics>Chapter 22 - Inverse Trigonometric Functions>Assignment>Q 58

If $\alpha =3{\cos }^{-1}\left(\frac{5}{\sqrt{28}}\right)+3{\tan }^{-1}\left(\frac{\sqrt{3}}{2}\right)$ and $\beta =4{\sin }^{-1}\left(\frac{7\sqrt{2}}{10}\right)-4{\tan }^{-1}\left(\frac{3}{4}\right)$ then value of $5\cos \alpha +10\sec \beta$ is equal to

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IMPORTANT

Gamma Question Bank for Engineering Mathematics>Chapter 22 - Inverse Trigonometric Functions>Assignment>Q 59

The range of $f\left(x\right)={\cot }^{-1}\left(\frac{x^2}{1+x^2}\right)$ is $\left(a,b\right)$ then $\frac{3\pi }{a+b}$ is equal to

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IMPORTANT

Gamma Question Bank for Engineering Mathematics>Chapter 22 - Inverse Trigonometric Functions>Assignment>Q 60

The number of positive integers in the domain of $f\left(x\right)={\cos }^{-1}\left(\left[e^x\right]-1\right)+{\sin }^{-1}\left(\left[e^x\right]\right)$, where $\left[·\right]$ represents greatest integer function, is equal to

HARD

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IMPORTANT

Gamma Question Bank for Engineering Mathematics>Chapter 22 - Inverse Trigonometric Functions>Assignment>Q 1

If $\left|{\cos }^{-1}\left(\frac{1-x^2}{1+x^2}\right)\right|<\frac{\pi }{3}$, then $x$ belongs to the interval

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IMPORTANT

Gamma Question Bank for Engineering Mathematics>Chapter 22 - Inverse Trigonometric Functions>Assignment>Q 2

The set of values of $x$ satisfying $\left|{\sin }^{-1}x\right|\le \left|{\cos }^{-1}x\right|$ is

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IMPORTANT

Gamma Question Bank for Engineering Mathematics>Chapter 22 - Inverse Trigonometric Functions>Assignment>Q 3

The solution of the equation ${\cos }^{-1}\left(x\sqrt{3}\right)+{\cos }^{-1}x=\frac{\pi }{2}$ is given by