$\tan 6^{\circ} \tan 42^{\circ} \tan 66^{\circ} \tan 78^{\circ} = $

If $\frac{\sin (A+B)}{\sin (A-B)}=\frac{\cos (C+D)}{\cos (C-D)}$,then $\tan A \cot B=$

Let $\theta, \phi \in [0, 2\pi]$ be such that $2 \cos \theta(1-\sin \phi) = \sin^2 \theta \left(\tan \frac{\theta}{2} + \cot \frac{\theta}{2}\right) \cos \phi - 1$,$\tan (2\pi - \theta) > 0$ and $-1 < \sin \theta < -\frac{\sqrt{3}}{2}$. Then $\phi$ cannot satisfy

If $0 \leq \theta \leq 2 \pi$,$0 \leq \alpha \leq 2 \pi$ and $\sec ^{2018} \theta + \operatorname{cosec}^{2018} \alpha = 2$,then the value of $\cos ^{2020} \theta + \sin ^{2022} \alpha =$

Evaluate: $\sqrt{\sin ^4 x+4 \cos ^2 x}-\sqrt{\cos ^4 x+4 \sin ^2 x}$

If $\sin^{2}(10^{\circ}) \sin(20^{\circ}) \sin(40^{\circ}) \sin(50^{\circ}) \sin(70^{\circ}) = \alpha - \frac{1}{16} \sin(10^{\circ})$,then $16 + \alpha^{-1}$ is equal to