MCQ
$2^{sin x}+2^{cos x}$ ની ન્યૂનતમ કિમત મેળવો
- ✓$2^{1-\frac{1}{\sqrt{2}}}$
- B$2^{-1+\sqrt{2}}$
- C$2^{1-\sqrt{2}}$
- D$2^{-1+\frac{1}{\sqrt{2}}}$
$\Rightarrow \frac{2^{\sin x}+2^{\cos x}}{2} \geq \sqrt{2^{\sin x} \cdot 2^{\cos x}}$
$\Rightarrow 2^{\sin x}+2^{\cos x} \geq 2^{1+\left(\frac{\sin x+\cos x}{2}\right)}$
$\Rightarrow \min \left(2^{\sin x}+2^{\cos x}\right)=2^{1-\frac{1}{\sqrt{2}}}$
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