In a triangle $ABC$,if $\frac{\sin A - \sin C}{\cos C - \cos A} = \cot B$,then $A, B, C$ are in

If $a=3, b=5, c=7$ are the sides of a triangle $ABC$,then $\cot A+\cot B+\cot C=$

In a $\triangle ABC$,$\angle C = 60^{\circ}$ and $\angle A = 75^{\circ}$. If $D$ is a point on $AC$ such that the area of $\triangle BAD$ is $\sqrt{3}$ times the area of $\triangle BCD$,then the measure of $\angle ABD$ is (in $^{\circ}$)

In a triangle $ABC$,if $r_1 = 2r_2 = 3r_3$,then $\sin A : \sin B : \sin C =$

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 $\Delta ABC$,$\frac{\cos \frac{1}{2}(B - C)}{\sin \frac{1}{2}A} = $