If `theta` is the angle between the unit vectors `veca and vecb`, then prove that
i. `cos((theta)/2)=1/2|veca+vecb|`
` ii. sin (theta/2)=1/2|veca-vecb|`

Explanation

To prove the given statements, we will use the properties of unit vectors and some trigonometric identities. Let's break down the proof into two parts.

### Part i: Prove that \( \cos\left(\frac{\theta}{2}\right) = \frac{1}{2} |\vec{a} + \vec{b}| \)

1. **Given Information**:
- Let \( \vec{a} \) and \( \vec{b} \) be unit vectors. Therefore, \( |\vec{a}| = 1 \) and \( |\vec{b}| = 1 \).
- The angle between the vectors \( \vec{a} \) and \( \vec{b} \) is \( \theta \).

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