If `f(x)=2(1+sin x),` then evaluate `f((pi)/(2))`.

Explanation

To evaluate \( f\left(\frac{\pi}{2}\right) \) for the function \( f(x) = 2(1 + \sin x) \), follow these steps:

### Step-by-Step Solution:

1. **Identify the function**:
We have the function defined as:
\[ f(x) = 2(1 + \sin x) \]

2. **Substitute \( x \) with \( \frac{\pi}{2} \)**:
We need to evaluate \( f\left(\frac{\pi}{2}\right) \):
\[ f\left(\frac{\pi}{2}\right) = 2\left(1 + \sin\left(\frac{\pi}{2}\right)\right) \]

3. **Calculate \( \sin\left(\frac{\pi}{2}\right) \)**:
We know from trigonometric values that:
\[ \sin\left(\frac{\pi}{2}\right) = 1 \]

4. **Substitute the value of \( \sin\left(\frac{\pi}{2}\right) \)**:
Now, substitute this value back into the function:
\[ f\left(\frac{\pi}{2}\right) = 2\left(1 + 1\right) \]

5. **Simplify the expression**:
Simplifying further gives:
\[ f\left(\frac{\pi}{2}\right) = 2 \times 2 = 4 \]

6. **Final answer**:
Therefore, the value of \( f\left(\frac{\pi}{2}\right) \) is:
\[ f\left(\frac{\pi}{2}\right) = 4 \]