In a triangle $ABC$,if $(a-b)(s-c)=(b-c)(s-a)$,then $r_1+r_3=$

If $\triangle ABC$ is right-angled at $C$,then the value of $\tan A + \tan B$ is

In $\triangle ABC$,if $3 \sin A + 4 \cos B = 6$ and $4 \sin B + 3 \cos A = 1$,then the $\angle C$ is

If $a \cos A = b \cos B$,then $\Delta ABC$ is

If angles $A$,$B$,and $C$ of a $\Delta ABC$ are $75^o$,$45^o$,and $60^o$ respectively,then the ratio of the areas of $\Delta OBC$,$\Delta COA$,and $\Delta AOB$ respectively is [where $O$ is the circumcentre of the triangle].

Let $P_1, P_2, P_3$ be the altitudes of a triangle $ABC$ from the vertices $A, B, C$ respectively. If $\Delta$ denotes the area of the triangle and $s$ is the semi-perimeter of the triangle, then $\frac{\cos A}{P_1} + \frac{\cos B}{P_2} + \frac{\cos C}{P_3} = $