The minimum value of `2^sinx+2^cosx `

Explanation

To find the minimum value of \(2^{\sin x} + 2^{\cos x}\), we can use the Arithmetic Mean-Geometric Mean (AM-GM) inequality. Here’s a step-by-step solution:

### Step 1: Apply the AM-GM Inequality
According to the AM-GM inequality, for any non-negative numbers \(a\) and \(b\):
\[ \frac{a + b}{2} \geq \sqrt{ab} \]
In our case, let \(a = 2^{\sin x}\) and \(b = 2^{\cos x}\). Thus, we have:
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