If \(\cosec x-\cot x=\frac{1}{3}\), what is the value of (\cosec x+\cot x)?यदि \(\cosec x-\cot x=\frac{1}{3}\), तो (\cosec x+\cot x) का मान क्या है?
Answer and explanationउत्तर और व्याख्या
Correct answer:सही उत्तर: 33
Using the identity \(\cosec^2 x-\cot^2 x=1\), we get \((\cosec x-\cot x)(\cosec x+\cot x)=1\). Given \(\cosec x-\cot x=\frac{1}{3}\), so \(\frac{1}{3}(\cosec x+\cot x)=1\). Therefore, \(\cosec x+\cot x=3\). The value \(\frac{1}{3}\) is the given expression; its reciprocal gives 3. Exam tip: recognise \(\cosec^2 x-\cot^2 x=1\) and multiply the conjugate expressions in such questions.सर्वसमिका \(\cosec^2 x-\cot^2 x=1\) से \((\cosec x-\cot x)(\cosec x+\cot x)=1\) मिलता है। दिया है \(\cosec x-\cot x=\frac{1}{3}\), अतः \(\frac{1}{3}(\cosec x+\cot x)=1\)। इसलिए \(\cosec x+\cot x=3\)। \(\frac{1}{3}\) दिया हुआ व्यंजक है, उसका प्रतिलोम लेने पर 3 प्राप्त होता है। परीक्षा टिप: ऐसे प्रश्नों में \(\cosec^2 x-\cot^2 x=1\) पहचानकर दोनों संयुग्म व्यंजकों का गुणनफल लें।
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