Questions in trigonometry

Select	Question
	If$\frac{2\sin \alpha }{\{1+\cos \alpha +\sin \alpha \}}=y,$then $\frac{\{1-\cos \alpha +\sin \alpha \}}{1+\sin \alpha }=$
	If $\tan \alpha =\frac{1}{7}$and $\sin \beta =\frac{1}{\sqrt{10}}\left( 0<\alpha ,\,\beta <\frac{\pi }{2} \right)$, then $2\beta $is equal to
	If $\cos (\theta -\alpha ),\ \cos \theta $and $\cos (\theta +\alpha )$are in H.P., then $\cos \theta \sec \frac{\alpha }{2}$is equal to
	If $\sin \theta +\sin \varphi =a$and $\cos \theta +\cos \varphi =b,$then $\tan \frac{\theta -\varphi }{2}$is equal to
	If $\tan A=\frac{1-\cos B}{\sin B},$find$\tan 2A$in terms of $\tan B$ and show that
	If $\sin \beta $is the geometric mean between $\sin \alpha $and $\cos \alpha ,$then $\cos 2\beta $is equal to
	$\frac{\sec 8A-1}{\sec 4A-1}=$
	If $\frac{\cos A}{\sin B\sin C}+\frac{\cos B}{\sin C\sin A}+\frac{\cos C}{\sin A\sin B}=$then $32\sin \left( \frac{A}{2} \right)\sin \left( \frac{5A}{2} \right)=$
	$\tan 15{}^\circ =$
	If $\tan \alpha =\frac{1}{7},\ \tan \beta =\frac{1}{3},$then $\cos 2\alpha =$