WBJEE · Maths · Sequences and Series
The minimum value of \(2^{\sin x}+2^{\cos x}\) is
- A \(2^{1-1 / \sqrt{2}}\)
- B \(2^{1+1 / \sqrt{2}}\)
- C \(2^{\sqrt{2}}\)
- D 2
Answer & Solution
Correct Answer
(A) \(2^{1-1 / \sqrt{2}}\)
Step-by-step Solution
Detailed explanation
We know that \(\mathrm{AM} \geq \mathrm{GM}\) \(\therefore \quad \frac{2^{\sin x}+2^{\cos x}}{2} \geq \sqrt{2^{\sin x} 2^{\cos x}}\) \(\Rightarrow 2^{\sin x}+2^{\cos x} \geq 2 \sqrt{2^{\sin x+\cos x}}\)…
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