Wiskunde Multiple Choice Vraag uit Gricha's Wiskundige Vragenbank

$\frac{\sin 70^{\circ}}{\sin 20^{\circ}}-\frac{\cos 70^{\circ}}{\cos 20^{\circ}}=$	A.	1
B.	2
C.	$\frac{2}{\sin 40^\circ}$
D.	$\frac{\sin 40^\circ}{2}$
E.	2.tan 50°

$\frac{\sin 70^{\circ}}{\sin 20^{\circ}}-\frac{\cos 70^{\circ}}{\cos 20^{\circ}}=\frac{\sin 70.\cos 20^\circ -\cos 70^{\circ}.\sin 20^{\circ}}{\sin 20^{\circ}\cdot \cos 20^{\circ}}=\frac{\sin (70^{\circ}-20^{\circ} )}{\sin 20^{\circ}\cdot \cos 20^{\circ}} =\frac{\sin 50^{\circ}}{\sin 20^{\circ}\cdot \cos 20^{\circ}} =\frac{}{} =\frac{2\cdot \cos 40^{\circ}}{2.\sin 20^{\circ}.\cos 20^{\circ}}=\frac{2\cdot \cos 40^{\circ}}{\sin 40^{\circ}} =2.\cot 40^{\circ}=2.\tan 50^{\circ}$