In $\triangle \mathrm{ABC}$, with usual notations, if $\cos \frac{B}{2}=\sqrt{\frac{c+a}{2 a}}$, then $a^2=$

In a triangle ABC with usual notations, $\cot \frac{\mathrm{A}}{2}+\cot \frac{\mathrm{B}}{2}+\cot \frac{\mathrm{C}}{2}=$

With usual notations, in $\triangle \mathrm{ABC}$, the lengths of two sides are 10 cm and 9 cm respectively. If angles $\mathrm{A}, \mathrm{B}, \mathrm{C}$ are in A.P. then perimeter of $\triangle \mathrm{ABC}$ is

In a triangle ABC , with usual notations, if $\mathrm{a}=5, \mathrm{~b}=4, \cos (\mathrm{~A}-\mathrm{B})=\frac{31}{32}$, then $\mathrm{c}=$