Find the value of $\cos \left({\sec }^{-1} x+{\mathrm{cosec}}^{-1} x\right), \left|x\right|\ge 1$.

Important Questions on Inverse Trigonometric Functions

EASY

12th ICSE

IMPORTANT

Understanding ISC Mathematics Class 12 Volume 1>Chapter 2 - Inverse Trigonometric Functions>EXERCISE 2.2

If the value of ${\tan }^{-1}\left(\sin \left(-\frac{\mathrm{\pi }}{2}\right)\right)$ is of the form of $\frac{\pi }{a}$, then the value of $a=$

MEDIUM

12th ICSE

IMPORTANT

Understanding ISC Mathematics Class 12 Volume 1>Chapter 2 - Inverse Trigonometric Functions>EXERCISE 2.2

Find the value of $\cos \left({\tan }^{-1}\frac{3}{4}\right)$.

MEDIUM

12th ICSE

IMPORTANT

Understanding ISC Mathematics Class 12 Volume 1>Chapter 2 - Inverse Trigonometric Functions>EXERCISE 2.2

Find the value of $\tan \left({\cos }^{-1}\frac{8}{17}\right)$.

MEDIUM

12th ICSE

IMPORTANT

Understanding ISC Mathematics Class 12 Volume 1>Chapter 2 - Inverse Trigonometric Functions>EXERCISE 2.2

Simplify the ${\tan }^{-1}\left(\frac{\sin x}{1+\cos x}\right)$. (in the form of $\frac{a}{b})$.

MEDIUM

12th ICSE

IMPORTANT

Understanding ISC Mathematics Class 12 Volume 1>Chapter 2 - Inverse Trigonometric Functions>EXERCISE 2.2

Simplify the ${\tan }^{-1}\left(\frac{x}{\sqrt{1-x^2}}\right), \left|x\right|<1$.

EASY

12th ICSE

IMPORTANT

Understanding ISC Mathematics Class 12 Volume 1>Chapter 2 - Inverse Trigonometric Functions>EXERCISE 2.2

Solve the equation for $x : {\tan }^{-1} x={\sin }^{-1}\left(\frac{1}{\sqrt{2}}\right)$.

MEDIUM

12th ICSE

IMPORTANT

Understanding ISC Mathematics Class 12 Volume 1>Chapter 2 - Inverse Trigonometric Functions>EXERCISE 2.2

Solve the equation for $x : \cos \left({\sin }^{-1} x\right)=\frac{1}{2}$.

EASY

12th ICSE

IMPORTANT

Understanding ISC Mathematics Class 12 Volume 1>Chapter 2 - Inverse Trigonometric Functions>EXERCISE 2.2

Solve the equation for $x : 4 {\sin }^{-1} x+{\cos }^{-1} x=\mathrm{\pi }$.