The value of sqrt{3} , text{cosec} , 20^circ | vedclass

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Question

(C) Let $E = \sqrt{3} \, 	ext{cosec} \, 20^\circ - 	ext{sec} \, 20^\circ = \frac{\sqrt{3}}{\sin 20^\circ} - \frac{1}{\cos 20^\circ}$ $E = \frac{\sqr

Vedclass · Accepted Answer

$4$

Vedclass · Answer

(C) Let $E = \sqrt{3} \, 	ext{cosec} \, 20^\circ - 	ext{sec} \, 20^\circ = \frac{\sqrt{3}}{\sin 20^\circ} - \frac{1}{\cos 20^\circ}$ $E = \frac{\sqrt{3} \cos 20^\circ - \sin 20^\circ}{\sin 20^\circ \cos 20^\circ}$ Multiply numerator and denominator by $2$: $E = \frac{2(\frac{\sqrt{3}}{2} \cos 20^\circ - \frac{1}{2} \sin 20^\circ)}{\frac{1}{2} (2 \sin 20^\circ \cos 20^\circ)}$ $E = \frac{4(\sin 60^\circ \cos 20^\circ - \cos 60^\circ \sin 20^\circ)}{\sin 40^\circ}$ $E = \frac{4 \sin(60^\circ - 20^\circ)}{\sin 40^\circ} = \frac{4 \sin 40^\circ}{\sin 40^\circ} = 4$

The value of $\sqrt{3} \, \text{cosec} \, 20^\circ - \text{sec} \, 20^\circ$ is:

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