Question

The solution of the differential equation $(1+\cos x)\frac{dy}{dx}=1-\cos x$ is

• A. $y=\tan \frac{x}{2}+x+c$
• B. $y=2\tan \frac{x}{2}-x+c$
• C. $y=\tan \frac{x}{2}-x+c$
• D. $y=x-2\tan \frac{x}{2}+c$

Answer 1

The correct option is B $y=2\tan \frac{x}{2}-x+c$

$(1+\cos x)\frac{dy}{dx}=1-\cos x$

$\Rightarrow \int dy=\int \frac{1-\cos x}{1+\cos x}dx$

$\Rightarrow \int dy=\int {\tan }^2\frac{x}{2}dx+c$

$\Rightarrow y=\int ({\sec }^2\frac{x}{2}-1)dx+c$

$\Rightarrow y=2\tan \frac{x}{2}-x+c$