$\tan 5x \tan 3x \tan 2x = ?$

The value of ${e^{{{\log }_{10}}\tan 1^\circ + {{\log }_{10}}\tan 2^\circ + {{\log }_{10}}\tan 3^\circ + ........... + {{\log }_{10}}\tan 89^\circ }}$ is

If $2 \sin \left(\frac{\pi}{2}\right) = x^{2} + \frac{1}{x^{2}}$,then the value of $\left(x - \frac{1}{x}\right)$ is

If $x = a \cos^3 \theta$ and $y = b \sin^3 \theta$,then:

Let $n$ be a positive integer such that $\sin \frac{\pi }{2^n} + \cos \frac{\pi }{2^n} = \frac{\sqrt{n}}{2}.$ Then

The value of $\sec ^{2} 12^{\circ}-\frac{1}{\tan ^{2} 78^{\circ}}$ is