Help with inverse in non-linear function

42 Views Asked by At

while I was studying a problem in multivariative calculus, I was faced by this: Find the inverse of $f(x,y) = (\sin(xy),x\cos(y))$. If we call $u = \sin(xy)$ and $v = x\cos(y)$ how to solve this system for $x$ and $y$? I cant get anything, the best I've got was $$ \frac{y}{\cos(y)} = \frac{arcsin(u)}{v}, $$ but I cant proceed. Can somebody help me with this? Thanks in advance!!