Two circles of radii 4cm and 1cm touch each other externally and `theta` is the angle contained by their direct common tangents. Find `sin (theta/2)+cos(theta/2) dot`

Explanation

To solve the problem, we need to find the value of \( \sin \left( \frac{\theta}{2} \right) + \cos \left( \frac{\theta}{2} \right) \) for two circles of radii 4 cm and 1 cm that touch each other externally.

### Step-by-Step Solution:

1. **Understanding the Configuration**:
- We have two circles: Circle A with radius \( R_1 = 4 \) cm and Circle B with radius \( R_2 = 1 \) cm.
- The circles touch each other externally, meaning the distance between their centers is \( R_1 + R_2 = 4 + 1 = 5 \) cm.

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