Question
Download Solution PDFयदि y = \(\rm {\rm{\;}}\frac{{\left( {sinx - cosx} \right)}}{{sin2x}} \) तब \(\rm \frac{{dy}}{{dx}}\) का मान ज्ञात करें।
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFउपयोग की गई अवधारणा:
त्रिकोणमिति सूत्र
sin 2x = 2sin x cos x
गणना:
y = \(\rm {\rm{\;}}\frac{{\left( {sinx - cosx} \right)}}{{sin2x}}\)
y = \(\rm \frac{{\left( {sinx - cosx} \right)}}{{2.sinx.cosx}}\)
⇒ y = \(\rm \frac{{sinx}}{{2.sinx.cosx}} - \;\frac{{cosx}}{{2.sinx.cosx}}\)
⇒ y = \(\rm \left( {\frac{1}{{2cosx}}} \right)\; - \left( {\frac{1}{{2sinx}}} \right)\)
⇒ y = \(\frac{1}{2}\) (secx - cosecx)
दोनों पक्षों में अवकलन करने पर, हमें मिलता है
⇒ \(\rm \frac{{dy}}{{dx}} = \frac{1}{2}\left[ {\frac{{d\left( {secx} \right)}}{{dx}} - \frac{{d\left( {cosecx} \right)}}{{dx}}} \right]\)
⇒ \(\rm \frac{{dy}}{{dx}} = \frac{1}{2}\left( {secx.tanx + cosecx.cotx} \right)\)
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