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

$\sin 36^\circ \sin 72^\circ \sin 108^\circ \sin 144^\circ = $

$\cos 2(\theta + \phi) - 4\cos (\theta + \phi)\sin \theta \sin \phi + 2\sin^2 \phi = $

The value of $\cos(18^{\circ}-A) \cdot \cos(18^{\circ}+A) - \cos(72^{\circ}-A) \cdot \cos(72^{\circ}+A)$ is:

If $(m + 2)\sin \theta + (2m - 1)\cos \theta = 2m + 1$,then which of the following is true?

Let $\alpha, \beta$ be two real numbers such that $\pi < (\alpha-\beta) < 3 \pi$. If $\sin \alpha+\sin \beta=\frac{-21}{65}$ and $\cos \alpha+\cos \beta=\frac{-27}{65}$,then $\cos \left(\frac{\beta-\alpha}{2}\right)=$