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Prove that (tan 5theta + tan 3theta)/(...

Prove that ` (tan 5theta + tan 3theta)/(tan 5theta - tan 3theta) = 4 cos 2theta cos 4theta`

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To prove that \[ \frac{\tan 5\theta + \tan 3\theta}{\tan 5\theta - \tan 3\theta} = 4 \cos 2\theta \cos 4\theta \] we will start with the left-hand side (LHS) and manipulate it step by step. ...
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