In a `DeltaABC,2asin^(2)C/2+2csin^(2)A/2=`

Options

A. 2(s-c)
B. 2(s-b)
C. 2(s-a)
D. s

Explanation

To solve the problem \( 2A \sin^2 \frac{C}{2} + 2C \sin^2 \frac{A}{2} \) in triangle \( ABC \), we can follow these steps:

### Step 1: Use the Half-Angle Identity
We know that:
\[ \sin^2 \frac{C}{2} = \frac{1 - \cos C}{2} \quad \text{and} \quad \sin^2 \frac{A}{2} = \frac{1 - \cos A}{2} \]
Substituting these identities into the expression gives:
...