take alook....

we have
$\displaystyle
v^2=mu(2/r - 1/a)
$
and
$\displaystyle
r= a(1-e cosE)
$
so
$\displaystyle
v=(mu)^1/2 (2/{a(1-e cosE)} - 1/a)^1/2
$

$\displaystyle
v=(mu)^1/2 ({2-1+e cosE}/{a(1-e cosE)})^1/2
$

$\displaystyle
v=(mu/a)^{1/2} \left(\frac{1+e\ \cos(E)}{1-e\ \cos(E)}\right)^{1/2}
$

is it true