In `DeltaABC`, Prove that:
`cosA+cosB+cosC=1+4sinA/2sinB/2sinC/2`

Explanation

To prove that in triangle \( \Delta ABC \), the equation \( \cos A + \cos B + \cos C = 1 + 4 \sin \frac{A}{2} \sin \frac{B}{2} \sin \frac{C}{2} \) holds, we can follow these steps:

### Step 1: Use the Angle Sum Property
In triangle \( ABC \), we know that the sum of the angles is \( A + B + C = 180^\circ \).

### Step 2: Rewrite \( \cos C \)
Using the identity \( \cos C = \cos(180^\circ - (A + B)) = -\cos(A + B) \). We can express \( \cos C \) in terms of \( A \) and \( B \).

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