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