In a $\triangle ABC$,if $r_1 > r_2 > r_3$,then which of the following is true?

In a triangle $ABC$,if $a \neq b$,then the value of $\frac{a \cos A - b \cos B}{a \cos B - b \cos A} + \cos C$ is:

In $\Delta ABC,$ $1 - \tan \frac{A}{2}\tan \frac{B}{2} = $

With usual notations,if the lengths of the sides of a triangle are $7 \text{ cm}$,$4\sqrt{3} \text{ cm}$,and $\sqrt{13} \text{ cm}$,then the measure of the smallest angle is

$p_1, p_2, p_3$ are altitudes of a triangle $ABC$ drawn from the vertices $A, B, C$ respectively. If $\Delta$ is the area of the triangle and $2s$ is the sum of the sides,then $\frac{1}{p_1} + \frac{1}{p_2} - \frac{1}{p_3} =$

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