Aspire Faculty ID #15270 · Topic: JAMIA MCA 2016 · Just now
JAMIA MCA 2016

If $\cos^{2}\theta + \sec^{2}\theta = a$, then …

Solution

$\cos^{2}\theta + \sec^{2}\theta = \cos^{2}\theta + \dfrac{1}{\cos^{2}\theta}$. Let $x = \cos^{2}\theta$. Then $a = x + \dfrac{1}{x}$. By AM ≥ GM, $x + \dfrac{1}{x} \ge 2$.
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