$a=cos^271^{\circ}-cos71^{\circ}=cos71^{\circ}(cos71^{\circ}-1)<0$
$\therefore \sqrt{a^2}=-a$
$b=sin17^{\circ}-\sqrt{sin17^{\circ}}=\sqrt{sin17^{\circ}}(sin17^{\circ}-1)<0$
$\therefore \sqrt{b^2}=-b$
$\frac{5}{2}+\frac{\sqrt{a^2}}{2a}+\frac{b}{\sqrt{b^2}}=\frac{5}{2}-\frac{1}{2}-1=1$