#### Answer

$\displaystyle \tan\frac{5A}{2}$

#### Work Step by Step

Comparing with the Half-Angle Identity
$\displaystyle \tan\frac{A}{2}=\pm\sqrt{\frac{1-\cos A}{1+\cos A}}$,
if we replace $A$ with $5A$ in the identity,
the RHS equals the given expression.
So, the LHS =$ \displaystyle \tan\frac{5A}{2}$