Question

Find the solution of $\frac{dy}{dx}\tan y=\sin (x+y)+\sin (x-y)$

• A. $\sec y=-2\cos x+c$
• B. $\sec y=2\cos x+c$
• C. $\sec y=4\cos x+c$
• D. $\sec y=-4\cos x+c$

Answer 1

The correct option is A $\sec y=-2\cos x+c$

$\frac{dy}{dx}\tan y=\sin (x+y)+\sin (x-y)$\
$\frac{dy}{dx}\tan y=2\sin y.\cos y$
$\sec y\tan ydy=2\sin xdx.$
Integrating,
$\int \sec y\tan ydy=\int 2\sin xdx.$
or $\sec y=-2\cos x+c$