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Trigonometry Practice Test 1

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Question : 10 of 40

Marks: +1, -0

The value of

(\sqrt{3}\csc 20^{\circ} - \sec 20^{\circ})

is:

2
$2 \sqrt{3}$
4
$\frac{\sqrt{8}}{2}$

Solution: 👈: Video Solution

(\sqrt{3}\csc 20^{\circ} - \sec 20^{\circ})

=\tan 60^{\circ}\csc 20^{\circ} - \sec 20^{\circ}

=\frac{\sin 60^{\circ}}{\cos 60^{\circ}} \cdot \frac{1}{\sin 20^{\circ}} - \frac{1}{\cos 20^{\circ}}

=\frac{\sin 60^{\circ} \cos 20^{\circ} - \cos 60^{\circ} \sin 20^{\circ}}{\cos 60^{\circ} \cdot \sin 20^{\circ} \cos 20^{\circ}}

=\frac{\sin (60^{\circ} - 20^{\circ})}{\frac{1}{2} \cdot \frac{1}{2} (2 \sin 20^{\circ} \cos 20^{\circ})}

=4\frac{\sin 40^{\circ}}{\sin 40^{\circ}}=4

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