In a $\triangle ABC$,if $a \cos^2 \frac{C}{2} + c \cos^2 \frac{A}{2} = \frac{3b}{2}$,then

If $2 \sin x - \cos 2x = 1$,then $(3 - 2 \sin^2 x) = $

In $\triangle PQR$,let $\angle P > \angle Q$. If the radian measures of $\angle P$ and $\angle Q$ satisfy the equation $4 \sin^3 x - 3 \sin x + a = 0$ where $0 < a < 1$,then the radian measure of $\angle R$ is

The angles $A, B$ and $C$ of a triangle $ABC$ are in $A.P.$ and $a : b = 1 : \sqrt{3}$. If $c = 4 \text{ cm}$,then the area (in $\text{sq. cm}$) of this triangle is:

The greatest angle of the triangle whose sides are $x^2+x+1$,$2x+1$,and $x^2-1$ is (in $^{\circ}$)

In an isosceles triangle $ABC$,$\angle C = \angle A$. If the point of intersection of the bisectors of internal angles $\angle A$ and $\angle C$ divides the median of side $AC$ in the ratio $3 : 1$ (from vertex $B$ to side $AC$),then the value of $\csc \frac{B}{2}$ is equal to