In a triangle $ABC$,with usual notations,$\cot \left(\frac{A+B}{2}\right) \cdot \tan \left(\frac{A-B}{2}\right) = $

With the usual notations,in a $\triangle ABC$,if $a=2, b=\sqrt{6}$ and $c=\sqrt{3}+1$,then $\sin^2 C - \sin^2 A =$

In $\Delta ABC$,if $\sin^{2} A + \sin^{2} B + \sin^{2} C = 2$,then the triangle is:

If the sides of a triangle are in the ratio $2 : \sqrt{6} : (\sqrt{3} + 1)$,then the largest angle of the triangle will be.....$^o$

If $a = 2, b = 3, c = 5$ in $\Delta ABC$,then $C = $

Consider a triangle $ABC$ and let $a, b$ and $c$ denote the lengths of the sides opposite to vertices $A, B$ and $C$ respectively. Suppose $a=6, b=10$ and the area of the triangle is $15 \sqrt{3}$. If $\angle ACB$ is obtuse and if $r$ denotes the radius of the incircle of the triangle,then $r^2$ is equal to