A) \[{{e}^{\cos x}}\tan \frac{y}{2}=c\]
B) \[{{e}^{\cos x}}\tan \,y=c\]
C) \[\cos x\tan y=c\]
D) \[\cos x\sin y=]c\]
Correct Answer: A
Solution :
[a] \[dy-\sin x\sin y\,dx=0\] Or \[dy=\sin x\sin y\,dx\] Or \[\int{\text{cosec}\,y\,dy=\int{\sin x\,dx}}\] Or \[\log \,\tan \frac{y}{2}=-\cos x+\log c\] Or \[\log \frac{\tan \frac{y}{2}}{c}=-\cos x\] Or \[\frac{\tan \frac{y}{2}}{c}={{e}^{-\cos x}}\] Or \[{{e}^{\cos x}}\tan \frac{y}{2}=c\]
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