If $$x=\sin \left(2 \tan ^{-1} 2\right), y=\cos \left(2 \tan ^{-1} 3\right)$$ and $$z=\sec \left(3 \tan ^{-1} 4\right)$$, then

In $$\triangle A B C$$, medians $$A D$$ and $$B E$$ are drawn. If $$A D=4, \angle D A B=\frac{\pi}{6}$$ and $$\angle A B E=\frac{\pi}{3}$$, then the area of $$\triangle A B C$$ is

In a $$\triangle A B C, 2 \Delta^2=\frac{a^2 b^2 c^2}{a^2+b^2+c^2}$$, then the triangle is

The sides of a triangle inscribed in a given circle subtend angles $$\alpha, \beta, \gamma$$ at the center. The minimum value of the AM of $$\cos \left(\alpha+\frac{\pi}{2}\right), \cos \left(\beta+\frac{\pi}{2}\right)$$ and $$\cos \left(\gamma+\frac{\pi}{2}\right)$$ is equal to