In $\triangle ABC$,with usual notations,$2ab \sin \frac{1}{2}(A+B-C) =$

In $\Delta ABC$,$c\cos (A - \alpha ) + a\cos (C + \alpha ) = $

If in a $\triangle ABC$,$s(s-a) = (s-b)(s-c)$,then

If $\triangle ABC$ is such that $\angle A=90^{\circ}$ and $\angle B \neq \angle C$,then $\frac{b^2+c^2}{b^2-c^2} \sin (B-C)$ is equal to

In a $\triangle ABC$,if $a \cos^2 \frac{C}{2} + c \cos^2 \frac{A}{2} = \frac{3b}{2}$,then the sides of the triangle are in

The lengths of the sides of a triangle are three consecutive natural numbers and its largest angle is twice the smallest one. Then the lengths of the sides of the triangle (in units) are