A) \[\log \,\tan y+\sin x=c\]
B) \[\log \,\tan \frac{y}{2}+2\sin x=C\]
C) \[\tan \frac{y}{2}+\log \sin x=C\]
D) None of these.
Correct Answer: B
Solution :
The equation is, \[\frac{dy}{dx}=\sin (x-y)-\sin (x+y)=2\cos x\sin (-y)\] \[\Rightarrow \,\,\frac{dy}{\sin y}+2\cos xdx=0\] \[\Rightarrow \,\int{\cos ec\,\,y\,\,dy+2\int{\cos x\,\,dx=c}}\] \[\Rightarrow \,\,\log \tan \frac{y}{2}+2\sin x=C\]
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