The expression $\frac{\tan(x - \frac{\pi}{2}) \cdot \cos(\frac{3\pi}{2} + x) - \sin^3(\frac{7\pi}{2} - x)}{\cos(x - \frac{\pi}{2}) \cdot \tan(\frac{3\pi}{2} + x)}$ simplifies to:

The value of $\tan \frac{\pi}{3} + 2 \tan \frac{2 \pi}{3} + 4 \tan \frac{4 \pi}{3} + 8 \tan \frac{8 \pi}{3}$ is equal to (in $\sqrt{3}$)

The expression $\frac{\tan \left( \frac{3\pi}{2} - \alpha \right) \cos \left( \frac{3\pi}{2} - \alpha \right)}{\cos (2\pi - \alpha )} + \cos \left( \alpha - \frac{\pi}{2} \right) \sin (\pi - \alpha ) + \cos (\pi + \alpha ) \sin \left( \alpha - \frac{\pi}{2} \right)$ when simplified reduces to:

Which of the following equations has no solution?

If $A, B, C, D$ are the angles of a cyclic quadrilateral taken in order,then $\cos(180^{\circ} + A) + \cos(180^{\circ} - B) + \cos(180^{\circ} - C) - \sin(90^{\circ} - D) =$

$\cos ^2 45^{\circ}+\cos ^2 135^{\circ}+\cos ^2 225^{\circ}+\cos ^2 315^{\circ} = $