Prove that: `(sinA+sin3A+sin5A+sin7A)/(cosA+cos3A+cos5A+cos7A)=tan4A`

Explanation

To prove that

\[ \frac{\sin A + \sin 3A + \sin 5A + \sin 7A}{\cos A + \cos 3A + \cos 5A + \cos 7A} = \tan 4A, \]

we will use the sum-to-product identities for sine and cosine.

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