Let f \left(\right. x \left.\right) = secx + 2 cos 2 x + 1 , x \in \left(\right. \frac{- \pi}{2} , \frac{\pi}{2} \left.\right) , the minimum value of f (x) is

Engineering

Mathematics

Arithmetic Mean Geometric Mean and Harmonic Mean

Question

Let $f (x) = secx + 2 \cos 2 x + 1, x \in (\frac{- π}{2}, \frac{π}{2})$ , the minimum value of f (x) is

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f (x) = sec x + 4cos² x – 1

$\frac{secx}{2}, \frac{secx}{2}, 4 \cos^{2} x, A . M . \geq G . M .$

sec x +4 cos² x $\geq$ 3

sec x + 4 cos² x – 1 $\geq$ 3 – 1