If $A = 580^o$ then which one of the following is true
$2\,\sin \left( {\frac{A}{2}} \right)\,\, = \,\,\sqrt {1 + \sin A} \, - \,\sqrt {1 - \sin A} $
$2\sin \left( {\frac{A}{2}} \right)\, = \,\, - \,\,\sqrt {1 + \sin A} \,\, + \,\sqrt {1 - \sin A} $
$2\sin \left( {\frac{A}{2}} \right)\, = \,\, - \,\,\sqrt {1 + \sin A} \,\, - \,\sqrt {1 - \sin A} $
$2\sin \left( {\frac{A}{2}} \right)\, = \,\,\,\,\sqrt {1 + \sin A} \,\, + \,\sqrt {1 - \sin A} $
$\frac{{\sec \,8\theta - 1}}{{\sec \,4\theta - 1}}$ is equal to
$\sin {163^o}\cos {347^o} + \sin {73^o}\sin {167^o} = $
$\tan \alpha + 2\tan 2\alpha + 4\tan 4\alpha + 8\cot \,8\alpha = $
If $\frac{\sqrt{2} \sin \alpha}{\sqrt{1+\cos 2 \alpha}}=\frac{1}{7}$ and $\sqrt{\frac{1-\cos 2 \beta}{2}}=\frac{1}{\sqrt{10}}$ $\alpha, \beta \in\left(0, \frac{\pi}{2}\right),$ then $\tan (\alpha+2 \beta)$ is equal to
The value of $\tan 7\frac{1}{2}^\circ $ is equal to