The value of frac{1}{sin 10^{circ}}-frac{sqrt | vedclass

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Question

(B) Given expression $= \frac{\cos 10^{\circ} - \sqrt{3} \sin 10^{\circ}}{\sin 10^{\circ} \cos 10^{\circ}}$Multiply the numerator and denominator by $

Vedclass · Accepted Answer

$4$

Vedclass · Answer

(B) Given expression $= \frac{\cos 10^{\circ} - \sqrt{3} \sin 10^{\circ}}{\sin 10^{\circ} \cos 10^{\circ}}$Multiply the numerator and denominator by $2$:$= \frac{2 \left( \frac{1}{2} \cos 10^{\circ} - \frac{\sqrt{3}}{2} \sin 10^{\circ} ight)}{\sin 10^{\circ} \cos 10^{\circ}}$Using $\sin 30^{\circ} = \frac{1}{2}$ and $\cos 30^{\circ} = \frac{\sqrt{3}}{2}$:$= \frac{2 (\sin 30^{\circ} \cos 10^{\circ} - \cos 30^{\circ} \sin 10^{\circ})}{\sin 10^{\circ} \cos 10^{\circ}}$Using the formula $\sin(A - B) = \sin A \cos B - \cos A \sin B$:$= \frac{2 \sin(30^{\circ} - 10^{\circ})}{\sin 10^{\circ} \cos 10^{\circ}} = \frac{2 \sin 20^{\circ}}{\sin 10^{\circ} \cos 10^{\circ}}$Multiply numerator and denominator by $2$ to use the identity $\sin 2	heta = 2 \sin 	heta \cos 	heta$:$= \frac{4 \sin 20^{\circ}}{2 \sin 10^{\circ} \cos 10^{\circ}} = \frac{4 \sin 20^{\circ}}{\sin 20^{\circ}} = 4$

The value of $\frac{1}{\sin 10^{\circ}}-\frac{\sqrt{3}}{\cos 10^{\circ}}=$

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