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What is the principal value of \(\sin^{-1}\left(\sin\left(-\frac{2\pi}{3}\right)\right)\)?\(\sin^{-1}\left(\sin\left(-\frac{2\pi}{3}\right)\right)\) का मुख्य मान क्या है?
Answer and explanationउत्तर और व्याख्या
Correct answer:सही उत्तर: -\(\frac{\pi}{3}\)-\(\frac{\pi}{3}\)
\(\sin\left(-\frac{2\pi}{3}\right)=-\frac{\sqrt{3}}{2}\), so the principal value is -\(\frac{\pi}{3}\). Keep the answer of \(\sin^{-1}x\) in \(-[\frac{\pi}{2},\frac{\pi}{2}]\).\(\sin\left(-\frac{2\pi}{3}\right)=-\frac{\sqrt{3}}{2}\), इसलिए मुख्य मान \(-\frac{\pi}{3}\) है। \(\sin^{-1}x\) का उत्तर हमेशा \([-\frac{\pi}{2},\frac{\pi}{2}]\) में रखें।
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