If in $\triangle A B C, B=45^{\circ}, a=2(\sqrt{3}+1)$ and area of $\triangle A B C$ is $6+2 \sqrt{3}$ sq. units, then the side $b=$

In a $\triangle A B C$, if $\sin ^2 B=\sin A$ and $2 \cos ^2 A=3 \cos ^2 B$, then the triangle is

In a $\triangle A B C$, if $A=30^{\circ}$ and $\frac{b}{(\sqrt{3}+1)^2+2(\sqrt{2}-1)} =\frac{c}{(\sqrt{3}+1)^2-2(\sqrt{2}-1)}$, then $B$

In $\triangle A B C$ is the line joining the circumcentre and the incentre is parallel to $B C$, then $\cos B+\cos C=$