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(sinx-sin3x)/(sin^(2)x-cos^(2)x) = 2sinx...

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

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To prove the equation \(\frac{\sin x - \sin 3x}{\sin^2 x - \cos^2 x} = 2 \sin x\), we will start with the left-hand side (LHS) and simplify it step by step. ### Step 1: Rewrite the numerator using the sine subtraction formula The numerator \(\sin x - \sin 3x\) can be rewritten using the sine subtraction formula: \[ \sin a - \sin b = 2 \cos\left(\frac{a+b}{2}\right) \sin\left(\frac{a-b}{2}\right) \] Here, \(a = x\) and \(b = 3x\). Thus, ...
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