In any triangle $ABC$,$(b+c) \cos A + (c+a) \cos B + (a+b) \cos C$ equals

If in triangle $ABC$,$\cos A = \frac{\sin B}{2\sin C}$,then the triangle is

Which of the following sets of data does not uniquely determine an acute-angled $\Delta ABC$ ($R$ = circum-radius)?

Let $ABC$ and $ABC^{\prime}$ be two non-congruent triangles with sides $AB=4$,$AC=AC^{\prime}=2\sqrt{2}$ and $\angle B=30^{\circ}$. The absolute value of the difference between the areas of these triangles is

In a $\Delta ABC$,if $b = a(\sqrt{3} - 1)$ and $\angle C = 30^o$,then the measure of the angle $A$ is.....$^o$.

In triangle $ABC$,$(b + c)\cos A + (c + a)\cos B + (a + b)\cos C = $