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Evaluate \(\sec^{-1}(2)\) using the principal value.principal value का प्रयोग करके \(\sec^{-1}(2)\) का मान निकालिए।
Answer and explanationउत्तर और व्याख्या
Correct answer:सही उत्तर: \(\frac{\pi}{3}\)\(\frac{\pi}{3}\)
Let \(\theta=\sec^{-1}(2)\). Then \(\sec\theta=2\), so \(\cos\theta=\frac{1}{2}\). In the principal range \([0,\pi]\), \(\cos\theta=\frac{1}{2}\) occurs at \(\theta=\frac{\pi}{3}\). Hence \(\sec^{-1}(2)=\frac{\pi}{3}\).मान लीजिए \(\theta=\sec^{-1}(2)\). तब \(\sec\theta=2\), इसलिए \(\cos\theta=\frac{1}{2}\). principal range \([0,\pi]\) में \(\cos\theta=\frac{1}{2}\) के लिए \(\theta=\frac{\pi}{3}\) मिलता है। अतः \(\sec^{-1}(2)=\frac{\pi}{3}\).
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