What is the principal value of \(\sec^{-1}\left(\frac{1}{2}\right)\) ?\(\sec^{-1}\left(\frac{1}{2}\right)\) का principal value क्या है?
Answer and explanationउत्तर और व्याख्या
Correct answer:सही उत्तर: \(\frac{\pi}{3}\)\(\frac{\pi}{3}\)
\(\sec^{-1}(1/2)=\theta\) means \(\sec\theta=\frac{1}{2}\). So \(\cos\theta=\frac{1}{2}\). The principal value for \(\sec^{-1}\) is taken in \([0,\pi]\). In this interval, \(\cos\theta=\frac{1}{2}\) occurs at \(\theta=\frac{\pi}{3}\). Hence \(\sec^{-1}\left(\frac{1}{2}\right)=\frac{\pi}{3}\).मान लीजिए \(\sec^{-1}(1/2)=\theta\). इसका अर्थ है \(\sec\theta=\frac{1}{2}\) । अतः \(\cos\theta=\frac{1}{2}\). \(\sec^{-1}\) का principal value \([0,\pi]\) अंतराल में लिया जाता है। इस अंतराल में \(\cos\theta=\frac{1}{2}\) के लिए \(\theta=\frac{\pi}{3}\) मिलता है। इसलिए \(\sec^{-1}\left(\frac{1}{2}\right)=\frac{\pi}{3}\).
Student feedback
Was this question useful?
👍 0 Helpful 👎 0 Not helpful
Yes 0% No 0%
0 responsesStudent Reviews
No published reviews yet.
