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What is the domain of \(\cosec^{-1}x\) ?\(\cosec^{-1}x\) का परिभाषा-क्षेत्र (domain) क्या है?
Answer and explanationउत्तर और व्याख्या
Correct answer:सही उत्तर: \(x\le -1\) or \(x\ge 1\)\(x\le -1\) या \(x\ge 1\)
Let \(y=\cosec^{-1}x\). Then \(x=\cosec y\). Since \(\cosec y=\frac{1}{\sin y}\), we must have \(\sin y\ne 0\), and also \(|\cosec y|\ge 1\). Therefore \(x\) must satisfy \(x\le -1\) or \(x\ge 1\).मान लें \(y=\cosec^{-1}x\). तब \(x=\cosec y\)। क्योंकि \(\cosec y=\frac{1}{\sin y}\), इसलिए \(\sin y\ne 0\) होना चाहिए और \(|\cosec y|\ge 1\) होता है। अतः \(x\) के लिए \(x\le -1\) या \(x\ge 1\) आवश्यक है।
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