In $\Delta ABC,$ $a\sin (B - C) + b\sin (C - A) + c\sin (A - B) = $

In $\triangle ABC$,if $b \cos \theta = c - a$,(where $\theta$ is an acute angle),then $(c - a) \tan \theta =$

In $\triangle ABC$,if $a=3, b=4, c=6$,then $\frac{\cot \frac{A}{2}+\cot \frac{B}{2}+\cot \frac{C}{2}}{\cot A+\cot B+\cot C}=$

If in $\Delta ABC$,$AB = 4$,$BC = 6$ and $AC = 5$,and $h_1, h_2, h_3$ are the lengths of the altitudes from vertices $A, B, C$ respectively,then the value of $(\frac{1}{h_1} + \frac{1}{h_2} - \frac{1}{h_3})$ is equal to-

In $\triangle ABC$,with usual notations,if $a^4+b^4+c^4-2a^2c^2-2c^2b^2=0$,then $\angle C = \dots$ (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 $........^{\circ}$