In ` A B C ,a , ca n dA` are given and `b_1,b_2` are two values of the third side `b` such that `b_2=2b_1dot` Then prove that `sinA=sqrt((9a^2-c^2)/(8c^2))`

Explanation

To prove that \( \sin A = \sqrt{\frac{9a^2 - c^2}{8c^2}} \) given the conditions in triangle \( ABC \) with sides \( a, b_1, b_2, c \) and the relationship \( b_2 = 2b_1 \), we can follow these steps:

### Step 1: Use the Cosine Rule
We start by applying the cosine rule in triangle \( ABC \):
\[ \cos A = \frac{b^2 + c^2 - a^2}{2bc} \]
We will use this formula for both \( b_1 \) and \( b_2 \).
...