The principal value of sin ^{-1}left(sin frac | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(A) We know that the range of the principal value branch of $\sin ^{-1} x$ is $[-\frac{\pi}{2}, \frac{\pi}{2}]$.Since $\frac{3 \pi}{4}$ does not lie i

Vedclass · Accepted Answer

$\frac{\pi}{4}$

Vedclass · Answer

(A) We know that the range of the principal value branch of $\sin ^{-1} x$ is $[-\frac{\pi}{2}, \frac{\pi}{2}]$.Since $\frac{3 \pi}{4}$ does not lie in the interval $[-\frac{\pi}{2}, \frac{\pi}{2}]$,we simplify the expression:$\sin ^{-1}\left(\sin \frac{3 \pi}{4}ight) = \sin ^{-1}\left[\sin \left(\pi - \frac{\pi}{4}ight)ight]$Using the identity $\sin(\pi - 	heta) = \sin 	heta$,we get:$= \sin ^{-1}\left(\sin \frac{\pi}{4}ight)$Since $\frac{\pi}{4} \in [-\frac{\pi}{2}, \frac{\pi}{2}]$,the expression simplifies to:$= \frac{\pi}{4}$

The principal value of $\sin ^{-1}\left(\sin \frac{3 \pi}{4}\right)$ is

Similar Questions

Solve $\sin(\tan^{-1} x)$,where $|x| < 1$,is equal to:

The principal value of $\sin ^{-1}\left(-\frac{1}{2}\right)$ is

Evaluate: $\cos^{-1}\sqrt{1-x} + \sin^{-1}\sqrt{1-x}$

Find the value of $\tan ^{-1}\left[2 \cos \left(2 \sin ^{-1} \frac{1}{2}\right)\right]$

If $f(x) = \frac{\sqrt{\operatorname{Cos}^{-1} x}}{\sqrt{2(1-x)}}$ for $x < 1$,then $\lim_{x \rightarrow 1^{-}} f(x) =$

Vedclass Test Series

Exam Paper Generator

Online Exam Module