If F = frac{2}{sin theta + sqrt{3} cos theta} | vedclass

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(C) The expression in the denominator is $f(	heta) = \sin 	heta + \sqrt{3} \cos 	heta$.We can rewrite this as $f(	heta) = 2 \left( \frac{1}{2} \si

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$1$

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(C) The expression in the denominator is $f(	heta) = \sin 	heta + \sqrt{3} \cos 	heta$.We can rewrite this as $f(	heta) = 2 \left( \frac{1}{2} \sin 	heta + \frac{\sqrt{3}}{2} \cos 	heta ight) = 2 \sin(	heta + 60^\circ)$.The range of $\sin(	heta + 60^\circ)$ is $[-1, 1]$.Therefore,the range of the denominator $f(	heta)$ is $[-2, 2]$.For $F$ to be minimum,the denominator must be at its maximum positive value,which is $2$.Thus,$F_{\min} = \frac{2}{2} = 1$.

If $F = \frac{2}{\sin \theta + \sqrt{3} \cos \theta}$,then the minimum value of $F$ is

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