In a `DeltaABC ,angleB=(2pi)/3` and cos A + cos c = `lamda`. Then , the exhaustive set of value of `lamda` is

Options

A. `(1,3//2]`
B. `(3//2,sqrt3)`
C. `(1//2,sqrt3//2)`
D. none of these

Explanation

To solve the problem, we need to find the exhaustive set of values for \( \lambda = \cos A + \cos C \) in triangle \( ABC \) where \( \angle B = \frac{2\pi}{3} \).

### Step-by-step Solution:

1. **Understand the Triangle Properties**:
In triangle \( ABC \), the sum of angles is \( \pi \). Therefore, we have:
\[
A + B + C = \pi
...