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  • If f(x) = cos2x + sec2x, then A. f(x) < 1 B. f(x) = 1 C. 2 < f(x) < 1 D. f(x) ≥ 2 [Hint: A.M ≥ G.M.]

If f(x) = \cos\textsuperscript{2}x + sec\textsuperscript{2}x, then

A. f(x) < 1\\\\

B. f(x) = 1\\\\

C. 2 < f(x) < 1\\\\

D. f(x) \geq 2\\\\

[Hint: A.M \geq G.M.]  

Answers (1)

The answer is the option (d) 

  \\ f \left( x \right) =\cos ^{2}x+\sec ^{2}x~~ \\\\ We~know~that AM \geq GM \\\\ \frac{ \left( \cos^{2}x+\sec ^{2}x \right) }{2} \geq \sqrt {\cos ^{2}xsec^{2}~x}~~~~ \\\\ ~~\frac{ \left( \cos^{2}x+\sec ^{2}x \right) }{2} \geq 1~ \\\\ ~~\cos ^{2}x+\sec ^{2}x \geq 2~ \\\\ \text{~ f} \left( x \right) \geq 2 \\\\

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infoexpert21

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