In $\Delta ABC$,$\frac{\sin B}{\sin (A + B)} = $

In $\triangle ABC$,if the median $AD$ drawn through $A$ is perpendicular to the side $AC$,then $3ca \cos A \cos C + 2a^2 =$

In a $\Delta ABC,$ if $b = 20, c = 21$ and $\sin A = 3/5$,then $a = $

In a $\triangle ABC$,if $\angle C = 90^{\circ}$,then $\frac{a^2-b^2}{a^2+b^2}$ is equal to

If $p_1, p_2, p_3$ are altitudes of a triangle $ABC$ from the vertices $A, B, C$ respectively and if $\Delta$ is the area of the triangle,$S$ is the semi-perimeter of the triangle,then find the value of $\frac{\cos A}{p_1} + \frac{\cos B}{p_2} + \frac{\cos C}{p_3}$.

In any $\triangle ABC$,$\frac{\cos A}{a} + \frac{\cos B}{b} + \frac{\cos C}{c} =$