Questions in trigonometry

Select	Question
	$\sin 75{}^\circ =$
	If $\tan \alpha =\frac{m}{m+1}$and $\tan \beta =\frac{1}{2m+1}$, then $\alpha +\beta =$
	$\tan 20{}^\circ +\tan 40{}^\circ +\sqrt{3}\tan 20{}^\circ \tan 40{}^\circ =$
	$\frac{1}{4}\left[ \sqrt{3}\cos 23{}^\circ -\sin 23{}^\circ \right]=$
	$\tan 75{}^\circ -\cot 75{}^\circ =$
	If $\tan A=-\frac{1}{2}$and $\tan B=-\frac{1}{3},$then $A+B=$
	If $A+B=225{}^\circ ,$then$\frac{\cot A}{1+\cot A}.\frac{\cot B}{1+\cot B}=$
	If $\sin A=\frac{4}{5}$and $\cos B=-\frac{12}{13},$where A and B lie in first and third quadrant respectively, then $\cos (A+B)=$
	If $A+B=\frac{\pi }{4},$then $(1+\tan A)(1+\tan B)=$
	$\frac{1}{\sin 10{}^\circ }-\frac{\sqrt{3}}{\cos 10{}^\circ }$=