Define a surface by

Show that, for

Enneper's surface has no self-intersections. Hint: use polar coordinates

and show

, and then show that the equality implies that points in the (u, v) plane on different circles about (0, 0) cannot be mapped to the same point.

So what i did was plug in

into the parametrization of the surface and like the problem suggested i took the x, y, and z, and plugged them into the expression as they wanted. after some tedious calculations i finally reduced the long expression down to

. when i match it up to the right side i see that everything is correct except the sines and cosines to the 4th power in the last term. however i done the problem many times and checked my work slowly along the way but i always get that the 4th power of sin and cos at the end that does not cancel out. can someone perform the calculation and see what one gets? i want to know whether it is the problem at fault or me at fault for making the same overlooked mistake over and over again.