If the solution of the different equation \( \frac{d y}{d x}=\frac{1}{x \cos y+\sin 2 y} \) is \...

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If the solution of the different equation \( \frac{d y}{d x}=\frac{1}{x \cos y+\sin 2 y} \) is \( x=c . e^{\sin y}-k(1+\sin y) \), then \( k \) equals
(a) 1
(b) 2
(c) 3
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