The value of sqrt{3} cot 20^{circ} - 4 cos 20 | vedclass

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(A) Let $E = \sqrt{3} \cot 20^{\circ} - 4 \cos 20^{\circ}$.$E = \sqrt{3} \frac{\cos 20^{\circ}}{\sin 20^{\circ}} - 4 \cos 20^{\circ}$$E = \frac{\sqrt{

Vedclass · Accepted Answer

$1$

Vedclass · Answer

(A) Let $E = \sqrt{3} \cot 20^{\circ} - 4 \cos 20^{\circ}$.$E = \sqrt{3} \frac{\cos 20^{\circ}}{\sin 20^{\circ}} - 4 \cos 20^{\circ}$$E = \frac{\sqrt{3} \cos 20^{\circ} - 4 \sin 20^{\circ} \cos 20^{\circ}}{\sin 20^{\circ}}$Using $2 \sin 	heta \cos 	heta = \sin 2	heta$,we get $4 \sin 20^{\circ} \cos 20^{\circ} = 2 \sin 40^{\circ}$.$E = \frac{\sqrt{3} \cos 20^{\circ} - 2 \sin 40^{\circ}}{\sin 20^{\circ}}$$E = \frac{\sqrt{3} \cos 20^{\circ} - 2 \sin(60^{\circ} - 20^{\circ})}{\sin 20^{\circ}}$$E = \frac{\sqrt{3} \cos 20^{\circ} - 2 (\sin 60^{\circ} \cos 20^{\circ} - \cos 60^{\circ} \sin 20^{\circ})}{\sin 20^{\circ}}$$E = \frac{\sqrt{3} \cos 20^{\circ} - 2 (\frac{\sqrt{3}}{2} \cos 20^{\circ} - \frac{1}{2} \sin 20^{\circ})}{\sin 20^{\circ}}$$E = \frac{\sqrt{3} \cos 20^{\circ} - \sqrt{3} \cos 20^{\circ} + \sin 20^{\circ}}{\sin 20^{\circ}}$$E = \frac{\sin 20^{\circ}}{\sin 20^{\circ}} = 1$.

List-$I$	List-$II$
$(I)$ $\sin^2 5^{\circ} + \sin^2 10^{\circ} + \sin^2 15^{\circ} + \dots + \sin^2 90^{\circ}$	$(A)$ $0$
$(II)$ $\tan^2 5^{\circ} \cdot \tan^2 10^{\circ} \cdot \tan^2 15^{\circ} \dots \tan^2 85^{\circ}$	$(B)$ $\frac{19}{2}$
$(III)$ $\cos^2 5^{\circ} + \cos^2 10^{\circ} + \cos^2 15^{\circ} + \dots + \cos^2 180^{\circ}$	$(C)$ $18$
$(IV)$ $\cot 5^{\circ} + \cot 10^{\circ} + \cot 15^{\circ} + \dots + \cot 175^{\circ}$	$(D)$ $1$
	$(E)$ $-1$

The value of $\sqrt{3} \cot 20^{\circ} - 4 \cos 20^{\circ}$ is equal to

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