int frac{dx}{cos x - sin x} का मान ज्ञात कीजि | vedclass

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Question

(A) माना $I = \int \frac{dx}{\cos x - \sin x}$.$\sqrt{2}$ से गुणा और भाग करने पर:$I = \frac{1}{\sqrt{2}} \int \frac{dx}{\frac{1}{\sqrt{2}} \cos x - \f

Vedclass · Accepted Answer

$\frac{1}{\sqrt{2}} \log \left| 	an \left( \frac{x}{2} + \frac{3\pi}{8} ight) ight| + c$

Vedclass · Answer

(A) माना $I = \int \frac{dx}{\cos x - \sin x}$.$\sqrt{2}$ से गुणा और भाग करने पर:$I = \frac{1}{\sqrt{2}} \int \frac{dx}{\frac{1}{\sqrt{2}} \cos x - \frac{1}{\sqrt{2}} \sin x}$$\cos \frac{\pi}{4} = \sin \frac{\pi}{4} = \frac{1}{\sqrt{2}}$ का उपयोग करने पर:$I = \frac{1}{\sqrt{2}} \int \frac{dx}{\cos x \cos \frac{\pi}{4} - \sin x \sin \frac{\pi}{4}} = \frac{1}{\sqrt{2}} \int \frac{dx}{\cos(x + \frac{\pi}{4})}$$I = \frac{1}{\sqrt{2}} \int \sec(x + \frac{\pi}{4}) dx$सूत्र $\int \sec 	heta d	heta = \log |	an(\frac{	heta}{2} + \frac{\pi}{4})| + c$ का उपयोग करने पर:$I = \frac{1}{\sqrt{2}} \log \left| 	an \left( \frac{x + \frac{\pi}{4}}{2} + \frac{\pi}{4} ight) ight| + c$$I = \frac{1}{\sqrt{2}} \log \left| 	an \left( \frac{x}{2} + \frac{\pi}{8} + \frac{2\pi}{8} ight) ight| + c$$I = \frac{1}{\sqrt{2}} \log \left| 	an \left( \frac{x}{2} + \frac{3\pi}{8} ight) ight| + c$.

$\int \frac{dx}{\cos x - \sin x}$ का मान ज्ञात कीजिए।

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