Question

$\frac{1}{\sin 10^{\circ }}-\frac{\sqrt{3}}{\cos 10^{\circ }}=$

• A. 0
• B. 1
• C. 2
• D. 4

Answer 1

Answer: (D)

$\frac{1}{\sin 10^{\circ }}-\frac{\sqrt{3}}{\cos 10^{\circ }}=\frac{\left[\cos 10^{\circ }-\sqrt{3}\sin 10^{\circ }\right]}{\sin 10^{\circ }\cos 10^{\circ }}$
$=\frac{2\left[\frac{1}{2}\cos 10^{\circ }-\frac{\sqrt{3}}{2}\sin 10^{\circ }\right]}{\sin 10^{\circ }\cos 10^{\circ }}$
$=\frac{2\left[\sin 30^{\circ }\cos 10^{\circ }-\cos 30^{\circ }\sin 10^{\circ }\right]}{\sin 10^{\circ }\cos 10^{\circ }}$
$=\frac{2\left[\sin \left(30^{\circ }-10^{\circ }\right)\right]}{\sin 10^{\circ }\cos 10^{\circ }}=\frac{2\cdot 2\sin \left(30^{\circ }-10^{\circ }\right)}{2\sin 10^{\circ }\cos 10^{\circ }}=4.$