(\sin^{-1}\(\sin x\)=x) कब सीधे सही माना जा सकता है?
When can (\sin^{-1}\(\sin x\)=x) be directly true?
Explanation opens after your attempt
A. जब \(x\in\left[-\frac{\pi}{2},\frac{\pi}{2}\right]\)When \(x\in\left[-\frac{\pi}{2},\frac{\pi}{2}\right]\)
Concept
The principal range of \(\sin^{-1}x\) is \(\left[-\frac{\pi}{2},\frac{\pi}{2}\right]\) so (\sin^{-1}\(\sin x\)=x) is directly true there. Without range it can be a mistake.
Why this answer is correct
The correct answer is A. जब \(x\in\left[-\frac{\pi}{2},\frac{\pi}{2}\right]\) / When \(x\in\left[-\frac{\pi}{2},\frac{\pi}{2}\right]\). The principal range of \(\sin^{-1}x\) is \(\left[-\frac{\pi}{2},\frac{\pi}{2}\right]\) so (\sin^{-1}\(\sin x\)=x) is directly true there. Without range it can be a mistake.
Exam Tip
\(\sin^{-1}x\) की प्रधान सीमा \(\left[-\frac{\pi}{2},\frac{\pi}{2}\right]\) है इसलिए इसी में (\sin^{-1}\(\sin x\)=x) सीधे सही है। सीमा के बिना यह गलती बन सकती है।
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