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

If $A$ is the solution set of the equation $\cos ^2 x = \cos ^2 \frac{\pi}{6}$ and $B$ is the solution set of the equation $\cos ^2 x = \log _{16} P$ where $P + \frac{16}{P} = 10$,then $B - A =$

The set of solutions of the system of equations $x+y = \frac{2 \pi}{3}$ and $\cos x + \cos y = \frac{3}{2}$,where $x, y$ are real,is

Let $PQR$ be a triangle of area $\Delta$ with $a=2, b=\frac{7}{2}$ and $c=\frac{5}{2}$,where $a, b$ and $c$ are the lengths of the sides of the triangle opposite to the angles at $P, Q$ and $R$ respectively. Then $\frac{2 \sin P-\sin 2P}{2 \sin P+\sin 2P}$ equals

In $\triangle ABC$,$\frac{a}{s-a}+\frac{b}{s-b}+\frac{c}{s-c} =$

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