If `a^2, b^2,c^2` are in A.P., then prove that `tanA ,tanB ,tanC` are in H.P.

Explanation

To prove that if \( A^2, B^2, C^2 \) are in Arithmetic Progression (A.P.), then \( \tan A, \tan B, \tan C \) are in Harmonic Progression (H.P.), we can follow these steps:

### Step-by-Step Solution:

1. **Understanding A.P. Condition**:
Since \( A^2, B^2, C^2 \) are in A.P., we can use the property of A.P. which states that the middle term is the average of the other two. Thus, we have:
\[
B^2 = \frac{A^2 + C^2}{2}
...