If $3 \sin \theta + 5 \cos \theta = 5$,then the value of $5 \sin \theta - 3 \cos \theta$ will be

If $\cos \alpha = \frac{2 \cos \beta - 1}{2 - \cos \beta}$,then the value of $\tan \frac{\alpha}{2} \cot \frac{\beta}{2}$ is,where $(0 < \alpha < \pi$ and $0 < \beta < \pi$).

If $\tan 3^{\circ} + 2\tan 6^{\circ} + 4\tan 12^{\circ} + 8\cot 24^{\circ} = \cot \theta^{\circ}$,then:

$\frac{\tan \theta}{1-\cot \theta}+\frac{\cot \theta}{1-\tan \theta}$ is equal to

$\frac{{\sqrt {1 + \sin x} + \sqrt {1 - \sin x} }}{{\sqrt {1 + \sin x} - \sqrt {1 - \sin x} }} = $ (when $x$ lies in $II^{nd}$ quadrant)

If $\sin \alpha = 1/\sqrt{5}$ and $\sin \beta = 3/5$,then $\beta - \alpha$ lies in the interval