3 (20^ ) -1 (20^ ) = - Vidyadip

MCQ

$\frac{\sqrt{3}}{\sin \left(20^{\circ}\right)}-\frac{1}{\cos \left(20^{\circ}\right)}=$

A
2
B
$\frac{2 \sin 20^{\circ}}{\sin 40^{\circ}}$
✓
4
D
$\frac{4 \sin 20^{\circ}}{\sin 40^{\circ}}$

✓

Answer

Correct option: C.

4

(C)
$\frac{\sqrt{3}}{\sin 20^{\circ}}-\frac{1}{\cos 20^{\circ}}$
$=\frac{\sqrt{3} \cos 20^{\circ}-\sin 20^{\circ}}{\sin 20^{\circ} \cos 20^{\circ}}$
$=\frac{2\left[\frac{\sqrt{3}}{2} \cos 20^{\circ}-\frac{1}{2} \sin 20^{\circ}\right]}{\frac{2}{2} \sin 20^{\circ} \cos 20^{\circ}}$
$=\frac{4 \cos \left(20^{\circ}+30^{\circ}\right)}{\sin 40^{\circ}}=\frac{4 \cos 50^{\circ}}{\sin 40^{\circ}}$
$=\frac{4 \sin 40^{\circ}}{\sin 40^{\circ}}$
= 4

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