If the angles $\mathrm{A}, \mathrm{B}$ and C of a triangle are in A.P. and if $\mathrm{a}, \mathrm{b}$ and c denote the length of the sides opposite to $\mathrm{A}, \mathrm{B}$ and C respectively, then the value of $\frac{a}{b} \sin 2 B+\frac{b}{a} \sin 2 A$ is

In a triangle $A B C$, with usual notations, if $a=5$, $\mathrm{b}=7 \sin \mathrm{~A}=\frac{3}{4}$, then total number of triangles possible are

In a triangle $A B C$, with usual notations, $\cot \left(\frac{A+B}{2}\right) \cdot \tan \left(\frac{A-B}{2}\right)=$

In a triangle ABC , with usual notations, $(\mathrm{a}+\mathrm{b}+\mathrm{c})(\mathrm{a}+\mathrm{b}-\mathrm{c})=3 \mathrm{ab}$, then $\angle \mathrm{C}=$