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

If in $$\Delta$$ABC, with usual notations, the angles are in A.P., then $$\mathrm{\frac{a}{c}}$$ sin 2 C + $$\mathrm{\frac{c}{a}}$$ sin 2 A =

With usual notations, perimeter of a triangle $$A B C$$ is 6 times the arithmetic mean of sine of its angles. If $$\mathrm{a}=1$$, then measure of angle $$\mathrm{A}=$$

With usual notations if the angles of a triangle are in the ratio 1 : 2 : 3, then their corresponding sides are in the ratio.