(1) Consider the points that satisfy sin(x)*cos(y)=1
(a) Find dy/dx. That I've done: y'(x)=cot(x)*cot(y)
(b) It turns out that no tangent lines are ever defined. Give two explanations why this is, one using dy/dx, and one using the actual description of the collection of points where sin(x)*cos(y)=1. This is where I have a problem. I've solved this: y=arccos(1/sin(x)) and x=arcsin(1/cos(y)). I don't know where to go from here. What points satisfy the equation? There could be infinitely many points the way I see it. Why are there no tangent lines? I don't get it. Any help appreciated!

Question

(1) Consider the points that satisfy sin(x)*cos(y)=1
(a) Find dy/dx. >>That I've done: y'(x)=cot(x)*cot(y)
(b) It turns out that no tangent lines are ever defined. Give two explanations why this is, one using dy/dx, and one using the actual description of the collection of points where sin(x)*cos(y)=1. >>This is where I have a problem. I've solved this: y=arccos(1/sin(x)) and x=arcsin(1/cos(y)). I don't know where to go from here. What points satisfy the equation? There could be infinitely many points the way I see it. Why are there no tangent lines? I don't get it. Any help appreciated!