The value of $2^{s i n x} + 2^{c o s x}$ is

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Solution

The correct option is B

Since AM of two positive numbers $\geq$ then G

$\frac{2^{s i n x} + 2^{c o s x}}{2} \geq \sqrt{2^{s i n x} . 2^{c o s x}}$

= $2^{\sqrt{s i n x + c o s x}} = \sqrt{2^{\sqrt{2} c o s (x - \frac{π}{4}}}$

$> \sqrt{2^{- \sqrt{2}}}$

$\Rightarrow$ $2^{s i n x} + 2^{c o s x} \geq {2.2}^{\frac{- 1}{\sqrt{2}}} = 2^{1 - \frac{1}{\sqrt{2}}}$

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