frac{sqrt{3}text{cosec } 20^{circ}-sec 20^{ci | vedclass

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(C) ધારો કે $E = \frac{\sqrt{3}	ext{cosec } 20^{\circ}-\sec 20^{\circ}}{\cos 20^{\circ}\cos 40^{\circ}\cos 60^{\circ}\cos 80^{\circ}}$.અંશનું સાદુંરૂ

Vedclass · Accepted Answer

$64$

Vedclass · Answer

(C) ધારો કે $E = \frac{\sqrt{3}	ext{cosec } 20^{\circ}-\sec 20^{\circ}}{\cos 20^{\circ}\cos 40^{\circ}\cos 60^{\circ}\cos 80^{\circ}}$.અંશનું સાદુંરૂપ આપતા: $\sqrt{3}	ext{cosec } 20^{\circ}-\sec 20^{\circ} = \frac{\sqrt{3}}{\sin 20^{\circ}} - \frac{1}{\cos 20^{\circ}} = \frac{\sqrt{3}\cos 20^{\circ} - \sin 20^{\circ}}{\sin 20^{\circ}\cos 20^{\circ}} = \frac{2\sin(60^{\circ}-20^{\circ})}{\sin 20^{\circ}\cos 20^{\circ}} = \frac{2\sin 40^{\circ}}{\sin 20^{\circ}\cos 20^{\circ}}$.છેદનું સાદુંરૂપ આપતા: $\cos 20^{\circ}\cos 40^{\circ}\cos 60^{\circ}\cos 80^{\circ} = \frac{1}{16}$.તેથી, $E = \frac{2\sin 40^{\circ} / (\sin 20^{\circ}\cos 20^{\circ})}{1/16} = \frac{4\sin 40^{\circ} / \sin 40^{\circ}}{1/16} = 4 	imes 16 = 64$.

$\frac{\sqrt{3}\text{cosec } 20^{\circ}-\sec 20^{\circ}}{\cos 20^{\circ}\cos 40^{\circ}\cos 60^{\circ}\cos 80^{\circ}}$ નું મૂલ્ય કેટલું થાય?

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