A) \[sec\text{ }y+2\text{ }cos\text{ }x=c\]
B) \[sec\text{ }y-2\text{ }cos\text{ }x=c\]
C) \[cos\text{ }y-2\text{ }sin\text{ }x=c\]
D) \[tan\text{ }y-2\text{ }sec\text{ }y=c\]
E) \[sec\text{ }y+2\text{ }sin\text{ }x=c\]
Correct Answer: A
Solution :
\[\because \]\[\frac{dy}{dx}\tan y=\sin (x+y)+\sin (x-y)\] \[\Rightarrow \] \[\frac{dy}{dx}\tan y=2\sin x\,\cos y\] \[\Rightarrow \] \[\int{\tan y\,\sec y\,dy}=2\int{\sin x\,dx}\] \[\Rightarrow \] \[\sec y+2\cos x=c\]
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