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

In $\triangle ABC$,the sum of the lengths of two sides is $x$ and the product of those lengths is $y$. If $c$ is the length of the third side and $x^2 - c^2 = y$,then the circumradius of the triangle is

In a $\Delta ABC$,the expression $\left( \frac{a^2}{\sin A} + \frac{b^2}{\sin B} + \frac{c^2}{\sin C} \right) \sin \frac{A}{2} \sin \frac{B}{2} \sin \frac{C}{2}$ simplifies to,where $\Delta$ is the area of the triangle.

In $\triangle ABC$,$(r_1+r_2) \operatorname{cosec}^2 \frac{C}{2} =$

With usual notations,in any $\triangle ABC$,if $a \cos B = b \cos A$,then the triangle is:

In $\triangle ABC$,if $s-a : s-b : s-c = 2 : 3 : 4$,then $\cot A : \cot C =$