What is the simplified value of \(\frac{\cosec^2 x-1}{\cot^2 x}\)?\(\frac{\cosec^2 x-1}{\cot^2 x}\) का सरल मान क्या है?
Answer and explanationउत्तर और व्याख्या
Correct answer:सही उत्तर: 11
Using the Pythagorean trigonometric identity \(\cosec^2 x=1+\cot^2 x\), we get \(\cosec^2 x-1=\cot^2 x\). Therefore, \(\frac{\cosec^2 x-1}{\cot^2 x}=\frac{\cot^2 x}{\cot^2 x}=1\), wherever the expression is defined. \(\cot^2 x\) is not the final answer because it is only the simplified numerator. Exam tip: remember \(\cosec^2 x=1+\cot^2 x\) alongside \(\sec^2 x=1+\tan^2 x\).पाइथागोरसीय त्रिकोणमितीय सर्वसमिका \(\cosec^2 x=1+\cot^2 x\) से \(\cosec^2 x-1=\cot^2 x\) मिलता है। अतः \(\frac{\cosec^2 x-1}{\cot^2 x}=\frac{\cot^2 x}{\cot^2 x}=1\), जहाँ व्यंजक परिभाषित है। \(\cot^2 x\) उत्तर नहीं है, क्योंकि यह केवल अंश का सरल रूप है। परीक्षा टिप: \(\cosec^2 x=1+\cot^2 x\) को \(\sec^2 x=1+\tan^2 x\) के साथ याद रखें।
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