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What is the period of the function \(\cosec x\)?फलन \(\cosec x\) का period (आवर्तकाल) क्या है?
Answer and explanationउत्तर और व्याख्या
Correct answer:सही उत्तर: \(2\pi\)\(2\pi\)
Since \(\cosec x=\dfrac{1}{\sin x}\) and \(\sin(x+2\pi)=\sin x\), we get
\[\cosec(x+2\pi)=\cosec x\]
where defined. Also, the smallest positive shift that keeps \(\sin x\) unchanged (not just up to sign across undefined points) is \(2\pi\). Therefore, the period is \(2\pi\).क्योंकि \(\cosec x=\dfrac{1}{\sin x}\) और \(\sin(x+2\pi)=\sin x\), इसलिए
\[\cosec(x+2\pi)=\cosec x\]
जहाँ परिभाषित है। साथ ही \(\sin x\) को वही रखने वाला सबसे छोटा धनात्मक period \(2\pi\) है। अतः period \(2\pi\) है।
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