In $\triangle ABC, (r_2+r_3) \operatorname{cosec}^2 \frac{A}{2} =$

In a triangle $ABC$ with usual notations,if $a, b, c$ are in arithmetic progression,then $\tan \frac{A}{2} \cdot \tan \frac{C}{2} =$

In a $\Delta ABC$,if two sides $b$ and $c$ and an angle $B$ are given.
Statement $-1$: Let $b = 5 \ cm, c = 3 \ cm$ and $\angle B = 60^\circ$. The total number of possible triangles is $2$.
Statement $-2$: If $c \sin B < b < c$ and $B$ is an acute angle,then there are two possible values of $\angle C$.

In a $\triangle ABC$ with $\angle A = 90^{\circ}$,$P$ is a point on $BC$ such that $PA:PB = 3:4$. If $AB = \sqrt{7}$ and $AC = \sqrt{5}$,then $BP:PC$ is

If the lengths of the sides of a triangle are $3, 5, 7,$ then the largest angle of the triangle is

In a triangle $ABC$,if $\frac{a}{\tan A}=\frac{b}{\tan B}=\frac{c}{\tan C}$,then $\cos^2 A + \cos^2 B + \cos^2 C =$