Question

Verify Euler's realtion for

z= tan(y/x) ,x ≠ 0

Answer 1

We have given that,

$z = f(x,y) = tan\dfrac{y}{x}$ $x \ne 0$

We have to prove that,

$x \dfrac{\delta f}{\delta x} + y \dfrac{\delta f}{\delta y} = -f$

Solving the LHS

$x \dfrac{\delta f}{\delta x} + y \dfrac{\delta f}{\delta y} = -\dfrac{y}{x}sec^2\dfrac{y}{x}+\dfrac{y}{x}sec^2\dfrac{y}{x} = 0$

which is not equal to RHS. Hence, Euler's relation is not valid.