Let $p_1,p_2,p_3$ be the altitudes of $\triangle ABC$ from vertices $A,B,C$ respectively, $\Delta$ is the area of the triangle,$R$ is the circumradius of the triangle,then$\frac{\cos A}{p_1}+\frac{\cos B}{p_2}+\frac{\cos C}{p_3}=$
$(A)\frac{1}{R}$
$(B)\frac{a^2+b^2+c^2}{2R}$
$(C)\frac{\Delta}{2R}$
$(D)$none of these
I found $p_1=2R(\cos A+\cos B\cos C),p_2=2R(\cos B+\cos A\cos C),p_3=2R(\cos C+\cos B\cos A)$
$\frac{\cos A}{p_1}+\frac{\cos B}{p_2}+\frac{\cos C}{p_3}=\frac{\cos A}{2R(\cos A+\cos B\cos C)}+\frac{\cos B}{2R(\cos B+\cos A\cos C)}+\frac{\cos C}{2R(\cos C+\cos B\cos A)}$
$\frac{\cos A}{2R(\sin B\sin C)}+\frac{\cos B}{2R(\sin A\sin C)}+\frac{\cos C}{2R(\sin B\sin A)}$
I am stuck here.