Differential Equations Question 346
Question: The solution of the differential equation $ (1+\cos x)dy=(1-\cos x)dx $ is
Options:
A) $ y=2\tan \frac{x}{2}-x+c $
B) $ y=2\tan x+x+c $
C) $ y=2\tan \frac{x}{2}+x+c $
D) $ y=x-2\tan \frac{x}{2}+c $
Show Answer
Answer:
Correct Answer: A
Solution:
Here $ \frac{dy}{dx}=\frac{1-\cos x}{1+\cos x}={{\tan }^{2}}\frac{x}{2} $
Therefore $ dy=( {{\sec }^{2}}\frac{x}{2}-1 )dx $
Now on integrating both the sides, we get $ y=2\tan \frac{x}{2}-x+c $ .
BETA
