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What is the value of \(cosec^2\theta-\cot^2\theta\) = ?यदि \(cosec^2 \theta-\cot^2 \theta\) = ? का मान ज्ञात करना हो, तो सही उत्तर क्या होगा?
Answer and explanationउत्तर और व्याख्या
Correct answer:सही उत्तर: 11
Using the trigonometric identity \(cosec^2\theta=1+\cot^2\theta\), we obtain \(cosec^2\theta-\cot^2\theta=(1+\cot^2\theta)-\cot^2\theta=1\). Hence, option A is correct. Option B is incorrect because the constant term 1 remains after the \(\cot^2\theta\) terms cancel. For exams, remember the direct identity \(cosec^2\theta-\cot^2\theta=1\).त्रिकोणमितीय पहचान \(cosec^2\theta=1+\cot^2\theta\) के अनुसार, \(cosec^2\theta-\cot^2\theta=(1+\cot^2\theta)-\cot^2\theta=1\)। इसलिए सही विकल्प A है। विकल्प B गलत है, क्योंकि \(\cot^2\theta\) के पद कटने के बाद स्थिर पद 1 बचता है। परीक्षा में पहचान \(cosec^2\theta-\cot^2\theta=1\) सीधे याद रखें।
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