Question

$\frac{d}{dx}\left(\frac{\cos x+\sin x}{\cos x-\sin x}\right)=$

• A. $\sec 2x\tan 2x$
• B. $2\sec 2x(\sec 2x+\tan 2x)$
• C. $\tan 2x$
• D. $\sec 2x(\sec 2x-\tan 2x)$

Answer 1

Answer: (B)

$2\sec 2x(\sec 2x+\tan 2x)$

$\frac{d}{dx}\left(\frac{\cos x+\sin x(\cos x+\sin x)}{\cos x-\sin x\cos x+\sin x}\right)$

$\frac{d}{dx}\left(\frac{{\cos }^{2}x+{\sin }^{2}x+\sin 2x}{\cos 2x}\right)$

$\frac{d}{dx}(\sec 2x+\tan 2x)$

$2{\sec }^{2}x{\tan }^{2}x+2{\sec }^{2}x$

$2\sec 2x(\tan 2x+\sec 2x)$