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