Solve for $y'\cos{y}=\sin(x+y)$

My attempt

$$y'\cos{y}=\sin x \cos y + \cos x \sin y$$

Divide both side by $\cos y$
$$\frac{dy}{dx}=\sin x + \cos x \tan y$$

Integrate both sides and I got

$$y = -\cos x + \int \cos x \tan y \,dx$$

As [Maximilian Janisch](https://math.stackexchange.com/users/631742/maximilian-janisch) said that $\int\cos() \tan(())d≠\sin() \tan(())$ I didn't know what to do next.