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...

In triangle ABC, with usual notations, if $(a+b+c)(a+b-c) = ab$, then the measure of angle C is...

In $\triangle ABC$, with usual notation, if $a = 13, b = 14, c = 15$, then the sum of the values of $\sin\left(\dfrac{A}{2}\right)$ and $\sin A$ is....