$3.)(10$ pts$)$ For the polar coordinate system $x=rcos,y=rsin,$ show that the Jacobian can be simplified to

$\frac{\text{d}\text{e}\text{l}(x,y)}{\text{d}\text{e}\text{l}(r,)}=r$

$($At some point you will use the identity $co{s}^2+si{n}^2=1).$