# Math Help - [SOLVED] Prove that if h(u,v)=f(sin u + cos v), then (h_u)sin v + (h_v)cos u=0.

1. ## [SOLVED] Prove that if h(u,v)=f(sin u + cos v), then (h_u)sin v + (h_v)cos u=0.

Prove that if $h(u,v)=f(\sin u + \cos v)$, then $h_u\sin v+h_v\cos u=0$.
I'm not sure where to start, here. I can find no strategic examples in the text. Any ideas would be much appreciated. Thanks!

2. Originally Posted by hatsoff
I'm not sure where to start, here. I can find no strategic examples in the text. Any ideas would be much appreciated. Thanks!

A good idea is to define $z=\sin u +\cos v$ , so $h(u,v)=f(z(u))$, and then:

$h_u=\frac{\partial f}{\partial z}\frac{\partial z}{\partial u}=\frac{\partial f}{\partial z}\cos u$

$h_v=\frac{\partial f}{\partial z}\frac{\partial z}{\partial v}=\frac{\partial f}{\partial z}(-\sin v)$

Well, now just put things together

Tonio