If the perimeter of the triangle $ABC$ is $50 \text{ cm}$,then $b \cos^2 \frac{C}{2} + c \cos^2 \frac{B}{2} =$

In $\triangle ABC$,$m \angle B = \frac{\pi}{3}$ and $m \angle C = \frac{\pi}{4}$. Let point $D$ divide $BC$ internally in the ratio $1:3$. Then,the value of $\frac{\sin(\angle BAD)}{\sin(\angle CAD)}$ is

In a triangle $PQR$,if $\sin P, \sin Q, \sin R$ are in $A.P.$,then

In a $\triangle ABC$,$2(bc \cos A + ca \cos B + ab \cos C) = ?$

In $\triangle ABC$,what is the value of $\cos A + \cos B + \cos C$?

In a $\triangle ABC$,it is known that $AB=AC$. Suppose $D$ is the mid-point of $AC$ and $BD=BC=2$. Then,the area of the $\triangle ABC$ is