For theta frac{pi}{3},the value of f(theta) | vedclass

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(D) Given $f(	heta) = \sec^2 	heta + \cos^2 	heta$. Using the Arithmetic Mean-Geometric Mean ($AM$-$GM$) inequality,we know that for positive real

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$[2, \infty)$

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(D) Given $f(	heta) = \sec^2 	heta + \cos^2 	heta$. Using the Arithmetic Mean-Geometric Mean ($AM$-$GM$) inequality,we know that for positive real numbers $a$ and $b$,$\frac{a+b}{2} \ge \sqrt{ab}$. Here,$f(	heta) = \sec^2 	heta + \cos^2 	heta \ge 2 \sqrt{\sec^2 	heta \cdot \cos^2 	heta} = 2 \sqrt{1} = 2$. Since $	heta > \frac{\pi}{3}$,$\sec 	heta > \sec(\frac{\pi}{3}) = 2$,so $\sec^2 	heta > 4$. As $	heta$ increases,$\sec^2 	heta$ increases towards $\infty$ and $\cos^2 	heta$ remains in the interval $[0, 1)$. Thus,the minimum value is $2$ and the function can take any value up to $\infty$. Therefore,the interval is $[2, \infty)$.

For $\theta > \frac{\pi}{3}$,the value of $f(\theta) = \sec^2 \theta + \cos^2 \theta$ always lies in the interval

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