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When can \(\sin^{-1}(\sin x)=x\) be directly true?\(\sin^{-1}(\sin x)=x\) कब सीधे सही माना जा सकता है?
Answer and explanationउत्तर और व्याख्या
Correct answer:सही उत्तर: When \(x\in\left[-\frac{\pi}{2},\frac{\pi}{2}\right]\)जब \(x\in\left[-\frac{\pi}{2},\frac{\pi}{2}\right]\)
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.\(\sin^{-1}x\) 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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