If $2 \cos \theta + \sin \theta = 1$ $\left( \theta \neq \frac{\pi}{2} \right)$,then $7 \cos \theta + 6 \sin \theta$ is equal to

Let $\alpha = 3 + 4 + 8 + 9 + 13 + 14 + \dots$ up to $40$ terms. If $(\tan \beta)^{1020}$ is a root of the equation $x^2 + x - 2 = 0$,where $\beta \in (0, \frac{\pi}{2})$,then $\sin^2 \beta + 3 \cos^2 \beta$ is equal to:

$\tan 9^{\circ}-\tan 27^{\circ}-\tan 63^{\circ}+\tan 81^{\circ}=$

If $\cosh 2x = 241$,then $\operatorname{coth} x$ is equal to

If $0 \leqslant x \leqslant \pi$ and $81^{\sin ^2 x} + 81^{\cos ^2 x} = 30$,then $x$ takes the value:

If $A = \frac{\sin 3^\circ}{\cos 9^\circ} + \frac{\sin 9^\circ}{\cos 27^\circ} + \frac{\sin 27^\circ}{\cos 81^\circ}$ and $B = \tan 81^\circ - \tan 3^\circ$,then $\frac{B}{A}$ is equal to . . . . . . .