Answer
See below.
Work Step by Step
$LHS=\frac{tan(u)-cot(u)}{tan(u)+cot(u)}+1=\frac{tan(u)-cot(u)}{tan(u)+cot(u)}+\frac{tan(u)+cot(u)}{tan(u)+cot(u)}=\frac{2tan(u)}{tan(u)+cot(u)}=\frac{2tan(u)}{tan(u)+cot(u)}\times\frac{sin(u)cos(u)}{sin(u)cos(u)}=\frac{2sin^2(u)}{sin^2(u)+cos^2(u)}=2sin^2(u)=RHS$
