In a triangle ABC with usual notations if, $\tan \left(\frac{\mathrm{B}-\mathrm{C}}{2}\right)=x \cot \frac{\mathrm{~A}}{2}$, then $x=$

With usual notations, the perimeter of a triangle ABC is 6 times the arithmetic mean of sine of its angles. If $\mathrm{a}=1$, then $\angle \mathrm{A}=$

In a triangle ABC , with usual notations, $\tan \left(\frac{\mathrm{A}}{2}\right)=\frac{5}{6}, \tan \left(\frac{\mathrm{C}}{2}\right)=\frac{2}{5}$, then

With usual notation, in triangle ABC , $\mathrm{m} \angle \mathrm{A}=30^{\circ}$ then the value of $\left(1+\frac{\mathrm{a}}{\mathrm{c}}+\frac{\mathrm{b}}{\mathrm{c}}\right)\left(1+\frac{\mathrm{c}}{\mathrm{b}}-\frac{\mathrm{a}}{\mathrm{b}}\right)$ is equal to