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

In $\triangle ABC$, with usual notations, if the sides $a$, $b$ and $c$ are in the ratio $18 : 17 : 7$, then $\cot\dfrac{A}{2} : \cot\dfrac{B}{2} : \cot\dfrac{C}{2} =$

In $\triangle ABC$, with usual notations, if $\Delta$ denotes the area of triangle $ABC$ then the value of $2s(b+c-a)\tan\left(\dfrac{A}{2}\right)$ is equal to $\ldots$

In $\triangle ABC$, if $\angle C = \dfrac{\pi}{3}$, then the value of $\cos^2 A + \cos^2 B + \cos A\cos B$ is...