frac{1}{sin 10^circ} - frac{sqrt{3}}{cos 10^c | vedclass

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Question

(D) Given expression: $\frac{1}{\sin 10^\circ} - \frac{\sqrt{3}}{\cos 10^\circ}$$= \frac{\cos 10^\circ - \sqrt{3} \sin 10^\circ}{\sin 10^\circ \cos 10

Vedclass · Accepted Answer

$4$

Vedclass · Answer

(D) Given expression: $\frac{1}{\sin 10^\circ} - \frac{\sqrt{3}}{\cos 10^\circ}$$= \frac{\cos 10^\circ - \sqrt{3} \sin 10^\circ}{\sin 10^\circ \cos 10^\circ}$Multiply numerator and denominator by $2$:$= \frac{2(\frac{1}{2} \cos 10^\circ - \frac{\sqrt{3}}{2} \sin 10^\circ)}{\sin 10^\circ \cos 10^\circ}$Using $\sin 30^\circ = \frac{1}{2}$ and $\cos 30^\circ = \frac{\sqrt{3}}{2}$:$= \frac{2(\sin 30^\circ \cos 10^\circ - \cos 30^\circ \sin 10^\circ)}{\sin 10^\circ \cos 10^\circ}$Using $\sin(A - B) = \sin A \cos B - \cos A \sin B$:$= \frac{2 \sin(30^\circ - 10^\circ)}{\sin 10^\circ \cos 10^\circ}$$= \frac{2 \sin 20^\circ}{\sin 10^\circ \cos 10^\circ}$Multiply numerator and denominator by $2$:$= \frac{4 \sin 20^\circ}{2 \sin 10^\circ \cos 10^\circ}$Using $\sin 2	heta = 2 \sin 	heta \cos 	heta$:$= \frac{4 \sin 20^\circ}{\sin 20^\circ} = 4$.

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

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