Prove that:`(sinx-sin3x)/(sin^2x-cos^2x)=2sinx`

Explanation

To prove that \(\frac{\sin x - \sin 3x}{\sin^2 x - \cos^2 x} = 2 \sin x\), we will follow these steps:

### Step 1: Rewrite the Denominator
We start with the left-hand side:
\[ \frac{\sin x - \sin 3x}{\sin^2 x - \cos^2 x} \]
Notice that the denominator can be rewritten using the identity \(\sin^2 x - \cos^2 x = -(\cos^2 x - \sin^2 x)\). Thus, we can factor out a negative sign:
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