A) \[\sec y-2\cos x=c\]
B) \[\sec y+2\cos x=c\]
C) \[\cos y-2\sin x=c\]
D) \[\sec y+2\sin x=c\]
Correct Answer: B
Solution :
[b]: Given, \[\tan y\frac{dy}{dx}=\sin (x+y)+sin(x-y)\] \[\tan y\frac{dy}{dx}=\sin (x+y)+\sin (x-y)\]\[=2\sin x\cos y\] \[\Rightarrow \]\[\tan y\sec ydy=2\sin xdx\] \[\Rightarrow \]\[\int_{{}}^{{}}{\tan y\sec ydy=2}\int_{{}}^{{}}{\sin xdx}\] \[\Rightarrow \]\[\sec y=-2\cos x+c\Rightarrow \sec y+2\cos x=c\]
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