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

In a $\triangle ABC$,if $\frac{a}{b^2-c^2} + \frac{c}{b^2-a^2} = 0$,then $B$ is equal to

What is the greatest angle of the triangle whose sides are $x^2+x+1, 2x+1, x^2-1$ (in $^{\circ}$)?

Let $a, b$ and $c$ be the lengths of the sides of a triangle $ABC$ such that $\frac{a+b}{7} = \frac{b+c}{8} = \frac{c+a}{9}$. If $r$ and $R$ are the inradius and circumradius of the triangle $ABC$,respectively,then the value of $\frac{R}{r}$ is equal to

If in a triangle $ABC$,$\frac{2 \cos A}{a} + \frac{\cos B}{b} + \frac{2 \cos C}{c} = \frac{a}{bc} + \frac{b}{ca}$,then the value of the angle $A$ is:

In any $\triangle ABC$,$\frac{\cos 2A}{a^2} - \frac{\cos 2B}{b^2} =$