In a `DeltaABC` ,which one of the following is true?

Options

A. `(b+c)cosA/2=asin((B+C)/2)`
B. `(b+c)cos((B+C)/2)=asinA/2`
C. `(b-c)cos((B-C)/2)=acosA/2`
D. `(b-c)cosA/2=asin((B-C)/2)`

Explanation

To solve the problem, we need to analyze the given options for triangle \( \Delta ABC \). We will check each option to determine which one is true.

### Step 1: Analyze Option 1
**Option 1:** \( b + c \cdot \cos\left(\frac{a}{2}\right) = a \cdot \sin\left(\frac{b+c}{2}\right) \)

- **Left Hand Side (LHS):**
\[
LHS = (b + c) \cdot \cos\left(\frac{a}{2}\right)
...