In a $\triangle ABC$,the expression $(a-b)^2 \cos^2 \frac{C}{2} + (a+b)^2 \sin^2 \frac{C}{2}$ is equal to:

In $\triangle ABC$,with usual notations,if $\frac{b+c}{11}=\frac{c+a}{12}=\frac{a+b}{13}$,then the value of $\cos A+\cos B+\cos C$ is

In a triangle $ABC$,let $AB = \sqrt{23}$,$BC = 3$,and $CA = 4$. Then the value of $\frac{\cot A + \cot C}{\cot B}$ is:

If one side of a triangle is double the other and the angles opposite to these sides differ by $60^{\circ}$,then the triangle is

In a triangle $ABC$, if $a=3, b=4$ and $\sin A=\frac{3}{4}$, then $\angle CBA = (\text{in } ^{\circ})?$

In a $\triangle ABC$,the altitudes from $B$ and $C$ to the opposite sides are not shorter than their respective opposite sides. Then,one of the angles of $\triangle ABC$ is $........^{\circ}$