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What is the simplified value of (\sin^2 x(1+\cot^2 x))?(\sin^2 x(1+\cot^2 x)) का सरल मान क्या है?
Answer and explanationउत्तर और व्याख्या
Correct answer:सही उत्तर: \(1\)\(1\)
Use the identity \(1+\cot^2 x=\cosec^2 x\). Thus, \(\sin^2 x(1+\cot^2 x)=\sin^2 x\cdot\cosec^2 x=\sin^2 x\cdot\frac{1}{\sin^2 x}=1\). Therefore, the correct answer is \(1\). \(\sin^2 x\) is only a factor, not the simplified value. Exam tip: When you see \(1+\cot^2 x\), recall the \(\cosec^2 x\) identity.पहचान \(1+\cot^2 x=\cosec^2 x\) का प्रयोग करें। अतः \(\sin^2 x(1+\cot^2 x)=\sin^2 x\cdot\cosec^2 x=\sin^2 x\cdot\frac{1}{\sin^2 x}=1\)। इसलिए सही उत्तर \(1\) है। \(\sin^2 x\) केवल गुणनखंड है, सरल मान नहीं। परीक्षा टिप: \(1+\cot^2 x\) दिखते ही \(\cosec^2 x\) वाली पहचान याद करें।
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