In $\Delta ABC$,$2R^2 \sin A \sin B \sin C = $

In a $\triangle ABC$,if $a=4, b=5$ and $c=7$,then $\sin \left(\frac{A}{2}\right) = $

In a triangle $ABC$,if $b=7, c=4\sqrt{3}$ and $A=\frac{\pi}{6}$,then $a \sin B \sin C =$

If $p_1, p_2, p_3$ are altitudes of a triangle $ABC$ from the vertices $A, B, C$ respectively,and $\Delta$ is the area of the triangle,then $p_1^{-1} + p_2^{-1} - p_3^{-1}$ is equal to

Two sides of a triangle are given by the roots of the equation $x^2-5x+6=0$ and the angle between the sides is $\frac{\pi}{3}$. Then,the perimeter of the triangle is

Two sides of a triangle are $\sqrt{3}+1$ and $\sqrt{3}-1$ and the included angle is $60^{\circ}$. Find the difference of the remaining angles. (in $^{\circ}$)