In a triangle $ABC$,$r_1 \cot \frac{A}{2} + r_2 \cot \frac{B}{2} + r_3 \cot \frac{C}{2} =$

In a right-angled $\triangle ABC$, the measures of the angles are in an Arithmetic Progression ($A$.$P$.). If its smallest side is $4 \text{ units}$, then the area of $\triangle ABC$ is:

If in a triangle $ABC$,$\angle C = 60^{\circ}$,then $\frac{1}{a + c} + \frac{1}{b + c} = $

In a $\triangle ABC$,the expression $\frac{\cos C+\cos A}{c+a}+\frac{\cos B}{b}$ is equal to

If $\Delta = a^2 - (b - c)^2$,where $\Delta$ is the area of triangle $ABC$,then $\tan A$ is equal to

If in a $\Delta ABC$,$\cos 3A + \cos 3B + \cos 3C = 1$,then one angle must be exactly equal to .......$^o$