If $R$ is the circum radius of $\triangle A B C$, then $A(\triangle A B C)=\ldots \ldots$

In $\triangle A B C$, if $\tan A+\tan B+\tan C=6$ and $\tan A \cdot \tan B=2$ then $\tan C=$ ...........

In $\triangle A B C$; with usual notations, $$\frac{b \sin B-c \sin C}{\sin (B-C)}=\ldots \ldots$$

In $\triangle A B C$; with usual notations, if $\cos A=\frac{\sin B}{\sin C}$ then the triangle is ............