Number of solutions of $5 \cos^2 \theta - 3 \sin^2 \theta + 6 \sin \theta \cos \theta = 7$ in the interval $[0, 2 \pi]$ is:

If $ABC$ is a triangle of area $\Delta$ with $a = 2$, $b = \frac{7}{2}$, $c = \frac{5}{2}$, where $a, b, c$ are the lengths of the sides of the triangle opposite to angles $A, B$ and $C$ respectively, then $\frac{2 \sin A - \sin 2A}{2 \sin A + \sin 2A}$ is equal to...

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

In a triangle $ABC$,if $\cos A \cos B + \sin A \sin B \sin C = 1$,then $a : b : c =$

In a triangle $ABC$,$\left(\tan \frac{A}{2} \tan \frac{B}{2} \tan \frac{C}{2}\right)^2 \leq$

The sides of a triangle are $\sin \theta, \cos \theta$ and $\sqrt{1 + \sin \theta \cos \theta}$ for some $0 < \theta < \frac{\pi}{2}$. Then the greatest angle of the triangle is: