With usual notations,in $\triangle ABC$,if $a=2, b=3, c=5$ and $\frac{\cos A}{a}+\frac{\cos B}{b}+\frac{\cos C}{c}=\frac{k+7}{30}$,then $k=$

If in a triangle the angles are in $A.P.$ and $b:c = \sqrt{3}:\sqrt{2}$,then $\angle A$ is equal to .....$^o$.

In a triangle $ABC$ with usual notations,if $\tan A, \tan B, \tan C$ are in $H.P.$,then $a^{2}, b^{2}, c^{2}$ are in

In a $\triangle ABC$,$\cos \left(\frac{B+2C+3A}{2}\right) + \cos \left(\frac{A-B}{2}\right)$ is equal to

$A$ triangle $ABC$ has area of $P$ square units and perimeter $2S$ units. If $h_1, h_2$ and $h_3$ are respectively the lengths of the altitudes of the triangle drawn from the vertices $A, B$ and $C$,then $P^2 \left[ \frac{(h_1 h_2 + h_2 h_3 + h_3 h_1)^2}{h_1^2 h_2^2 h_3^2} - 2 \right] =$

In $\triangle ABC$,if $R = \frac{65}{8}$,$rr_1 = 42$ and $r_1 - r = 6.5$,then $s(s-a) = $