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?