In $\Delta ABC$,$(a-b)^2 \cos^2 \frac{C}{2} + (a+b)^2 \sin^2 \frac{C}{2} =$

If $H$ is the orthocentre of $\triangle ABC$ and $AH=x, BH=y, CH=z$,then $\frac{abc}{xyz}=$

$p_1, p_2, p_3$ are altitudes of a triangle $ABC$ drawn from the vertices $A, B, C$ respectively. If $\Delta$ is the area of the triangle and $2s$ is the sum of the sides,then $\frac{1}{p_1} + \frac{1}{p_2} - \frac{1}{p_3} =$

Let $ABC$ be a triangle with $\angle C=90^{\circ}$. Draw $CD$ perpendicular to $AB$. Choose points $M$ and $N$ on sides $AC$ and $BC$ respectively such that $DM$ is parallel to $BC$ and $DN$ is parallel to $AC$. If $DM=5$ and $DN=4$,then $AC$ and $BC$ are respectively equal to:

In any triangle $ABC$,what is the value of $a(b \cos C - c \cos B)$?

In any triangle,if the angles are in the ratio $1: 2: 3$,then their corresponding sides are in the ratio.