If `sin^2(A/2), sin^2(B/2), and sin^2(C/2)` are in `H.P.`, then prove that the sides of triangle are in `H.P.`

Explanation

To prove that if \( \sin^2\left(\frac{A}{2}\right), \sin^2\left(\frac{B}{2}\right), \sin^2\left(\frac{C}{2}\right) \) are in Harmonic Progression (H.P.), then the sides of the triangle \( a, b, c \) are also in H.P., we can follow these steps:

### Step-by-Step Solution:

1. **Understanding H.P.**:
We start with the condition that \( \sin^2\left(\frac{A}{2}\right), \sin^2\left(\frac{B}{2}\right), \sin^2\left(\frac{C}{2}\right) \) are in H.P. This means that the reciprocals \( \frac{1}{\sin^2\left(\frac{A}{2}\right)}, \frac{1}{\sin^2\left(\frac{B}{2}\right)}, \frac{1}{\sin^2\left(\frac{C}{2}\right)} \) are in Arithmetic Progression (A.P.).

2. **Using the Half-Angle Formula**:
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