A) \[{{e}^{\cos x}}\cdot \tan \frac{y}{2}=C\]
B) \[{{e}^{\cos x}}\cdot \tan y=C\]
C) \[\cos x\cdot \tan y=C\]
D) \[\cos x\cdot \sin y=C\]
Correct Answer: A
Solution :
Given equation can be rewritten as \[\cos ec\,\,y\,\,dy=\sin x\,\,dx\] On integrating both sides, we get \[\log \,\,\tan \frac{y}{2}=-\cos x+\log C\] \[\Rightarrow \] \[\log \frac{\tan \frac{y}{2}}{C}=-\cos x\] \[\Rightarrow \] \[\frac{\tan \frac{y}{2}}{C}={{e}^{-\cos x}}\] \[\Rightarrow \] \[{{e}^{\cos x}}\cdot \tan \frac{y}{2}=C\]
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