I am trying to convert dxdy in cartesian into polar plane.

and have to prove: dxdy = rd dr

Here is my conversion proof:

x = rcos

y = rsin

dx = -rsin d + cos dr

dy = rcos d + sin dr

ignoring 2nd order differentials, and keeping only drd ,

we have:

dxdy = -rsin d sin dr

+ rcos drcos d

= rd dr(-sin + cos )

I need to equate (-sin + cos ) = 1,

but i can't because of the -ve sign. Where did I go wrong?

Thanks for your time.