$1 + \cos 2x + \cos 4x + \cos 6x = $

In the graph of the function $\sqrt{3} \sin x + \cos x$,the maximum distance of a point from the $x$-axis is:

The value of $\sin 105^{\circ} + \cos 105^{\circ}$ is

If $A + B + C = \pi$ and $\cos A = \cos B \cos C$,then $\tan B \tan C$ is equal to

If $\tan \alpha = \frac{x^2 - x}{x^2 - x + 1}$ and $\tan \beta = \frac{1}{2x^2 - 2x + 1}$ $(x \ne 0, 1)$,where $0 < \alpha, \beta < \frac{\pi}{2}$,then $\tan(\alpha + \beta)$ has the value equal to:

The value of $\sin ^{2} 30^{\circ} \cos ^{2} 45^{\circ}+5 \tan ^{2} 30^{\circ}+\frac{3}{2}\sin ^{2} 90^{\circ}-3 \cos ^{2} 90^{\circ}$ is