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

In a triangle ABC , with usual notations, $\tan \left(\frac{\mathrm{A}}{2}\right)=\frac{5}{6}, \tan \left(\frac{\mathrm{C}}{2}\right)=\frac{2}{5}$, then

With usual notation, in triangle ABC , $\mathrm{m} \angle \mathrm{A}=30^{\circ}$ then the value of $\left(1+\frac{\mathrm{a}}{\mathrm{c}}+\frac{\mathrm{b}}{\mathrm{c}}\right)\left(1+\frac{\mathrm{c}}{\mathrm{b}}-\frac{\mathrm{a}}{\mathrm{b}}\right)$ is equal to

In $\triangle A B C$, with usual notations, $a \cos B=b \cos A, a \cos C \neq c \cos A$ then $\mathrm{A}(\triangle \mathrm{ABC})$ $\qquad$ sq. units.