Question

The solution of the differential equation $ \left( \frac{dy}{dx} \right)\tan y=\sin (x+y)+\sin (x-y) $ is

• A. $ sec\text{ }x-1/2\text{ }tan\text{ }y=c $
• B. $ log\text{ }sin\text{ (}x+y)=c $
• C. $ sec\text{ }x+tan\text{ }y=c $
• D. $ sec\text{ }y+2\text{ }cos\text{ }x=c $

Answer 1

Answer: (D)

Given, differential equation is
$ \left( \frac{dy}{dx} \right)\tan y=\sin (x+y)+\sin (x-y) $
$ \Rightarrow $ $ \left( \frac{dy}{dx} \right)\tan y=2\sin x\cos y $
$ \Rightarrow $ $ \frac{\sin y}{{{\cos }^{2}}y}dy=2\sin xdx $
On integrating both sides, we get $ \frac{1}{\cos y}=-2\cos x+c $
$ \Rightarrow $ $ \sec y+2\cos x=c $