The minimum value of 2^{sin x}+2^{cos x} is | vedclass

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Question

Usnign $AM \geq GM$

$\Rightarrow \frac{2^{\sin x}+2^{\cos x}}{2} \geq \sqrt{2^{\sin x} \cdot 2^{\cos x}}$

$\Rightarrow 2^{\sin x}+2^{\cos x} \ge

Vedclass · Accepted Answer

$2^{1-\frac{1}{\sqrt{2}}}$

Vedclass · Answer

Usnign $AM \geq GM$

$\Rightarrow \frac{2^{\sin x}+2^{\cos x}}{2} \geq \sqrt{2^{\sin x} \cdot 2^{\cos x}}$

$\Rightarrow 2^{\sin x}+2^{\cos x} \geq 2^{1+\left(\frac{\sin x+\cos x}{2}\right)}$

$\Rightarrow \min \left(2^{\sin x}+2^{\cos x}\right)=2^{1-\frac{1}{\sqrt{2}}}$

The minimum value of $2^{sin x}+2^{cos x}$ is

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