In $\Delta ABC$,find the value of $\frac{1}{a}\cos^2\frac{A}{2} + \frac{1}{b}\cos^2\frac{B}{2} + \frac{1}{c}\cos^2\frac{C}{2}$.

If the angles $A, B$ and $C$ of a triangle are in an Arithmetic Progression and if $a, b$ and $c$ denote the lengths of the sides opposite to $A, B$ and $C$ respectively,then the value of the expression $\frac{a}{c} \sin 2C + \frac{c}{a} \sin 2A$ is

In $\triangle ABC$,if $\sin^2 B = \sin C$ and $3 \cos^2 B = 2 \cos^2 C$,then $\triangle ABC$ is

If $7 \cos \theta - \sin \theta = 5$ and $\tan \theta > 0$,then $\tan \theta =$

In $\triangle ABC$,if $a, b$ and $c$ are in arithmetic progression,then $\cos A + 2 \cos B + \cos C =$

If $p_1, p_2, p_3$ are the altitudes and $a=4, b=5, c=6$ are the sides of a triangle $ABC$,then $\frac{1}{p_1^2} + \frac{1}{p_2^2} + \frac{1}{p_3^2} =$