Questions in trigonometry

Select	Question
	If $\frac{\pi }{2}<\alpha <\pi ,\,\text{ }\pi <\beta <\frac{3\pi }{2};$ $\sin \alpha =\frac{15}{17}$ and $\tan \beta =\frac{12}{5}$, then the value of $\sin (\beta -\alpha )$ is
	If $\cos x+\cos y+\cos \alpha =0$ and $\sin x+\sin y+\sin \alpha =0,$ then $\cot \,\left( \frac{x+y}{2} \right)=$
	If $\sin \theta +\sin 2\theta +\sin 3\theta =\sin \alpha $ and $\cos \theta +\cos 2\theta +\cos 3\theta =\cos \alpha $, then $\theta$ is equal to
	$\frac{\cos {{10}^{o}}+\sin {{10}^{o}}}{\cos {{10}^{o}}-\sin {{10}^{o}}}=$
	If $\cos P=\frac{1}{7}$ and $\cos Q=\frac{13}{14},$ where P and Q both are acute angles. Then the value of $P-Q$ is
	$\sec {{50}^{o}}+\tan {{50}^{o}}$ is equal to
	If $\tan \alpha ={{(1+{{2}^{-x}})}^{-1}},$ $\tan \beta ={{(1+{{2}^{x+1}})}^{-1}}$, then $\alpha +\beta $ equals
	The sum $S=\sin \theta +\sin 2\,\theta +....+\sin \,n\theta ,$ equals
	The value of $\cot {{70}^{o}}+4\cos {{70}^{o}}$ is
	The expression $2\cos \frac{\pi }{13}.\cos \frac{9\pi }{13}+\cos \frac{3\pi }{13}+\cos \frac{5\pi }{13}$ is equal to