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

In a triangle $ABC$,if $(a-b)(s-c)=(b-c)(s-a)$,then $r_1+r_3=$

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...

Let $S = \left\{ \theta \in [-\pi, \pi] - \left\{ \pm \frac{\pi}{2} \right\} : \sin \theta \tan \theta + \tan \theta = \sin 2 \theta \right\}$. If $T = \sum_{\theta \in S} \cos 2 \theta$,then $T + n(S)$ is equal to:

In any triangle $ABC$,find the value of $\cos ^2 \frac{A}{2}+\cos ^2 \frac{B}{2}+\cos ^2 \frac{C}{2}$.

If in a triangle $ABC$,$b \cos^2 \frac{A}{2} + a \cos^2 \frac{B}{2} = \frac{3}{2} c$,then $a, b, c$ are in: