If $\sin \theta + \text{cosec} \theta = 2$,then $\sin^2 \theta + \text{cosec}^2 \theta = $

Evaluate: $(\cos 252^{\circ} - \sin 126^{\circ})(\cos 252^{\circ} + \sin 126^{\circ})(\sin^2 126^{\circ} + \sin^2 186^{\circ} + \sin^2 66^{\circ})$

If $\cos A+\cos (A+B)+\cos (A+2 B)+\ldots$ up to $n$ terms $=$ $\cos \left(\frac{2 A+(n-1) B}{2}\right) \sin \frac{n B}{2} \operatorname{cosec} \frac{B}{2}$,then $\cos \frac{\pi}{19}+\cos \frac{3 \pi}{19}+\cos \frac{5 \pi}{19}+\ldots+\cos \frac{17 \pi}{19} = $

Factorize the expression: $\sec ^2 x+5 \tan x+5$

The value of $\frac{4 \sin 9^{\circ} \sin 21^{\circ} \sin 39^{\circ} \sin 51^{\circ} \sin 69^{\circ} \sin 81^{\circ}}{\sin 54^{\circ}}$ is equal to

If $\sin x + \sin^{2} x = 1$,then the value of $\cos^{8} x + 2 \cos^{6} x + \cos^{4} x$ is