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When is \(\tan^{-1}(\tan\theta)=\theta\) definitely true?\(\tan^{-1}(\tan\theta)=\theta\) कब निश्चित रूप से सत्य है?
Answer and explanationउत्तर और व्याख्या
Correct answer:सही उत्तर: \(\theta\in(-\frac{\pi}{2},\frac{\pi}{2})\)\(\theta\in(-\frac{\pi}{2},\frac{\pi}{2})\)
The principal range of (\tan^{-1}x) is ((-\frac{\pi}{2},\frac{\pi}{2})). Since (\tan) is periodic, the principal interval is necessary.\(\tan^{-1}x\) का principal range \((-\frac{\pi}{2},\frac{\pi}{2})\) है। \(\tan\) period वाला है, इसलिए principal interval जरूरी है।
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