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

Explanation

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

### Step 1: Start with the left-hand side
We begin with the expression:
\[ \sin^4 A - \cos^4 A \]

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