First slide

Extreme values and Periodicity of Trigonometric functions

Question

If $A + B = \frac{π}{3}$ where $A, B \in R^{+}$ . Then the minimum value of $\sec A + \sec B$ is

Moderate

A

$\frac{2}{\sqrt{3}}$
B

$\frac{4}{\sqrt{3}}$
C

$2 \sqrt{3}$
D

none of these

Solution

For $y = \sec x, x \in (0, \frac{π}{2})$
$T a n g e n t d r a w n t o i t a t a n y p o i n t l i e s c o m p l e t e l y b e l o w t h e g r a p h o f$ $y = \sec x$
$∴ \frac{\sec A + \sec B}{2} \geq \sec (\frac{A + B}{2})$
$\Rightarrow \sec A + \sec B \geq 2. \sec (\frac{π}{6}) = \frac{4}{\sqrt{3}}$

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