If $a = 9, b = 8$ and $c = x$ satisfies $3 \cos C = 2$,then

In any triangle $ABC$,what is the value of $a(b \cos C - c \cos B)$?

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

In $\triangle ABC$,if $r_1=8, r_2=12$ and $r_3=24$,then the ordered triple $(a, b, c) =$

In a $\Delta ABC$,if $b + c = 3a$,then the value of $\cot\, \frac{B}{2} \cdot \cot\, \frac{C}{2}$ is equal to:

In a triangle $ABC$,with usual notation,$\angle B = \pi/3$ and $\angle C = \pi/4$. If $D$ divides $BC$ internally in the ratio $1:3$,find the value of $\frac{\sin \angle BAD}{\sin \angle CAD}$.