\(\sin^{-1}(\sin\theta)=\theta\) कब निश्चित रूप से सत्य है?
When is \(\sin^{-1}(\sin\theta)=\theta\) definitely true?
Explanation opens after your attempt
Correct Answer
B. \(\theta\in[-\frac{\pi}{2},\frac{\pi}{2}]\)
Concept
The output of \(\sin^{-1}x\) lies in \([-\frac{\pi}{2},\frac{\pi}{2}]\). Therefore \(\theta\) must lie in this range.
Why this answer is correct
The correct answer is B. \(\theta\in[-\frac{\pi}{2},\frac{\pi}{2}]\). The output of \(\sin^{-1}x\) lies in \([-\frac{\pi}{2},\frac{\pi}{2}]\). Therefore \(\theta\) must lie in this range.
Exam Tip
\(\sin^{-1}x\) का आउटपुट \([-\frac{\pi}{2},\frac{\pi}{2}]\) में होता है। इसलिए \(\theta\) इसी range में होना चाहिए।
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