Answer
See below.
Work Step by Step
$LHS=\frac{(sec(v)-tan(v))^2+1}{csc(v)(sec(v)-tan(v))}=\frac{sec^2(v)-2sectan(v)+tan^2(v)+1}{csc(v)(sec(v)-tan(v))}=\frac{sec^2(v)-2sectan(v)+sec^2(v)}{csc(v)(sec(v)-tan(v))}=\frac{2sec(v)(sec(v)-tan(v))}{csc(v)(sec(v)-tan(v))}=\frac{2sin(v)}{cos(v)}=2tan(v)=RHS$
