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

Let $A, B$ and $C$ be three angles of a $\triangle ABC$ such that $\cos A + \cos B + \cos C = \frac{3}{2}$,then the $\triangle ABC$ is

Let $ABC$ be a triangle such that $\angle ACB = \frac{\pi}{6}$ and let $a, b$ and $c$ denote the lengths of the sides opposite to $A, B$ and $C$ respectively. The value$(s)$ of $x$ for which $a = x^2+x+1, b = x^2-1$ and $c = 2x+1$ is (are)

If in a $\Delta ABC$,$\angle A = 45^\circ$,$\angle C = 60^\circ$,then $a + c\sqrt{2} = $

In $\triangle ABC$,if $\frac{1}{b+c} + \frac{1}{c+a} = \frac{3}{a+b+c}$,then $\angle C$ is equal to: (in $^{\circ}$)

In a triangle $ABC$,if $B = 3C$,then the values of $\sqrt{\frac{b + c}{4c}}$ and $\frac{b - c}{2c}$ are