Consider the parametric curve x = [1+cos(t)]cos(t), y = [1+sin(t)]cos(t).

Find dy/dx for a general t.

I have done the work and gotten:

dy/dx = y'(t)/x'(t) = [cos(t) - 1]/[-sin(t) + (1 + 2 cos(t))]

To me, this seems too long, but I can't see any way of simplifying it. If there is a way of simplifying it, could someone point it out to me. Thanks.