With usual notations,in $\Delta ABC$,if $b \cos ^{2} \frac{C}{2}+c \cos ^{2} \frac{B}{2}=\frac{3 a}{2}$,then

If $ABC$ is a triangle of area $\Delta$ with $a = 2$, $b = \frac{7}{2}$, $c = \frac{5}{2}$, where $a, b, c$ are the lengths of the sides of the triangle opposite to angles $A, B$ and $C$ respectively, then $\frac{2 \sin A - \sin 2A}{2 \sin A + \sin 2A}$ is equal to...

In a triangle $ABC$,if $a < b < c$ and $\frac{a^3+b^3+c^3}{\sin^3 A+\sin^3 B+\sin^3 C}=8$,then the maximum value of $c$ is

If the reciprocals of the lengths of the sides of a $\triangle ABC$ are in harmonic progression,then its ex-radii $r_1, r_2, r_3$ are in

In $\triangle ABC$,we are given that $3 \sin A + 4 \cos B = 6$ and $4 \sin B + 3 \cos A = 1$. Then,the measure of $\angle C$ is $....^{\circ}$

In $\triangle PQR$,if $\angle R = \frac{\pi}{4}$ and $\tan(\frac{P}{3})$,$\tan(\frac{Q}{3})$ are the roots of the equation $ax^2 + bx + c = 0$,then: