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Question
If f(x) = cos2x + sec2x, then ______.
[Hint: A.M ≥ G.M.]
Options
f(x) < 1
f(x) = 1
2 < f(x) < 1
f(x) ≥ 2
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Solution
If f(x) = cos2x + sec2x, then f(x) ≥ 2.
Explanation:
Given that: f(x) = cos2x + sec2x
We know that AM ≥ GM
⇒ `(cos^2 x + sec^2x)/2 ≥ sqrt(cos^2x . sec^2x)`
⇒ `(cos^2x + sec^2)/2 ≥ 1`
⇒ cos2x + sec2x ≥ 2
⇒ f(x) ≥ 2
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