Prove the following identities: `sin^4A+cos^4A=1-2sin^2Acos^2A`

Explanation

To prove the identity \( \sin^4 A + \cos^4 A = 1 - 2 \sin^2 A \cos^2 A \), we will start from the left-hand side and manipulate it to reach the right-hand side.

### Step-by-Step Solution:

1. **Start with the left-hand side:**
\[ \sin^4 A + \cos^4 A \]
...