In a $\Delta ABC$,the expression $\frac{\cos C + \cos A}{c + a} + \frac{\cos B}{b}$ is equal to:

In a triangle $ABC$,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 $^{\circ}$)

In $\triangle ABC$,if $a: b: c = 4: 5: 6$,then $\frac{\cos A + 3 \cos C}{\cos B} = $

In a $\Delta ABC$,the expression $\left( \frac{a^2}{\sin A} + \frac{b^2}{\sin B} + \frac{c^2}{\sin C} \right) \sin \frac{A}{2} \sin \frac{B}{2} \sin \frac{C}{2}$ simplifies to,where $\Delta$ is the area of the triangle.

If $\triangle ABC$ is a non-isosceles triangle and $\angle C = 90^{\circ}$,then $\frac{a^2+b^2}{a^2-b^2} \sin(A-B) = $

With usual notations, in $\triangle ABC$, if $\cos C = \frac{\sin A}{2 \sin B}$, then which of the following is true?