A) \[\sec y+2\cos x=c\]
B) \[\sec y-2\cos x=c\]
C) \[\cos y-2\sin x=c\]
D) \[\tan y-2\sec y=c\]
E) \[\sec y+2\sin x=c\]
Correct Answer: A
Solution :
\[\frac{dy}{dx}\tan y=\sin (x+y)+\sin (x-y)\] \[\frac{dy}{dx}(\tan y)=2\sin x\cos y\] Þ \[\frac{\sin y}{{{\cos }^{2}}y}dy=2\sin xdx\] Þ \[\int{\frac{\sin y}{{{\cos }^{2}}y}}dy=2\int{\sin xdx}\] Þ \[\frac{1}{\cos y}=-2\cos x+c\] \ \[\sec y+2\cos x=c\].
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