Simplify each expression.
±√[(1 - cos 5A)/(1 + cos 5A)]

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Recognize that the expression involves a square root of a fraction with trigonometric functions: \(\pm \sqrt{\frac{1 - \cos 5A}{1 + \cos 5A}}\).

Recall the trigonometric identity for tangent in terms of cosine: \(\tan^2 \theta = \frac{1 - \cos 2\theta}{1 + \cos 2\theta}\). Notice the similarity between this identity and the given expression.

Set \(\theta = \frac{5A}{2}\) so that \(2\theta = 5A\). Substitute into the identity to rewrite the expression inside the square root as \(\tan^2 \left( \frac{5A}{2} \right)\).

Since the square root of \(\tan^2 \left( \frac{5A}{2} \right)\) is \(|\tan \left( \frac{5A}{2} \right)|\), and the original expression includes \(\pm\), the simplified form is \(\pm \tan \left( \frac{5A}{2} \right)\).

Therefore, the original expression simplifies to \(\pm \tan \left( \frac{5A}{2} \right)\), using the tangent half-angle identity.

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