Implicit Differentiation and Tangent Lines

I. Differentiating $\cos(x)+\cos(y)=1$ implicitly results in $-\sin(x)-\sin(y)*(dy/dx)=0$.

II. Solving yields $dy/dx=-\frac{\sin(x)}{\sin(y)}$.

III. At a point where $\sin(y)=0$, the tangent line to the curve is horizontal.

Which of the above statements is/are true?