Discussion

The value of \(\tan 1° \tan 2° \tan 3° ... \tan 89°\) is:

Answer: B

We use the complementary angle identity \(\tan(90° - \theta) = \cot \theta\), and the fact that \(\tan \theta \cdot \cot \theta = 1\).

The expression can be paired up: \((\tan 1° \tan 89°) (\tan 2° \tan 88°) ...\)

Since \(\tan 89° = \tan(90°-1°) = \cot 1°\), the first pair is \(\tan 1° \cot 1° = 1\).

All pairs will multiply to 1. The middle term is \(\tan 45°\), which is also 1.

The final product is 1.

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