Question

$ \frac{1}{\cos 80{}^\circ }-\frac{\sqrt{3}}{\sin 80{}^\circ } $ is equal to:

• A. $ \sqrt{2} $
• B. $ \sqrt{3} $
• C. 2
• D. 4

Answer 1

The Correct Option is D

$ \frac{\sin 80{}^\circ -\cos 80{}^\circ \sqrt{3}}{\sin 80{}^\circ \cos 80{}^\circ } $
$=\frac{2\left[ \frac{1}{2}\sin 80{}^\circ -\frac{\sqrt{3}}{2}\cos 80{}^\circ \right]}{\sin 80{}^\circ \cos 80{}^\circ } $
$=\frac{4[\sin (80{}^\circ -60{}^\circ )]}{2\sin 80{}^\circ \cos 80{}^\circ } $
$=\frac{4\sin 20{}^\circ }{2\sin 80{}^\circ }=\frac{4\sin 20{}^\circ }{\sin (\pi -20{}^\circ )}=4 $