If in a triangle a `cos^2C/2+cos^2A/2=(3b)/2,` then find the relation between the sides of the triangle.

Explanation

To solve the problem, we start with the given equation:

\[ A \cos^2\left(\frac{C}{2}\right) + C \cos^2\left(\frac{A}{2}\right) = \frac{3B}{2} \]

### Step 1: Rewrite the cosine terms
Using the identity for cosine squared, we can express \(\cos^2\left(\frac{C}{2}\right)\) and \(\cos^2\left(\frac{A}{2}\right)\):
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