Questions in trigonometry

Select	Question
	If $\cos (A+B)=\alpha \cos A\cos B+\beta \sin A\sin B,$then $(\alpha ,\beta )$=
	$\frac{{{\sin }^{2}}A-{{\sin }^{2}}B}{\sin A\cos A-\sin B\cos B}=$
	If $\cos (\alpha +\beta )=\frac{4}{5},\sin (\alpha -\beta )=\frac{5}{13}$ and $\alpha ,\beta $ lie between 0 and $\frac{\pi }{4},$then $\tan 2\alpha =$
	If $\cos \theta =\frac{8}{17}$ and $\theta $ lies in the 1st quadrant, then the value of $\cos (30{}^\circ +\theta )+\cos (45{}^\circ -\theta )+\cos (120{}^\circ -\theta )$ is
	If $\tan x+\tan \left( \frac{\pi }{3}+x \right)+\tan \left( \frac{2\pi }{3}+x \right)=3,$ then
	The value of $\sin {{47}^{o}}+\sin 61{}^\circ -\sin 11{}^\circ -\sin 25{}^\circ =$
	If $\sin (\theta +\alpha )=a$ and $\sin (\theta +\beta )=b,$ then $\cos 2\,(\alpha -\beta )-4ab\,\cos (\alpha -\beta )$ is equal to
	The expression ${{\cos }^{2}}(A-B)+{{\cos }^{2}}B-2\cos (A-B)\cos A\cos B$ is
	The value of $\cos 15{}^\circ -\sin 15{}^\circ $is equal to
	If $\tan \alpha ,\tan \beta $are the roots of the equation ${{x}^{2}}+px+q=0\text{ }(p\ne 0),$ then