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Find the value of the product tan(60 deg)*tan(42 deg)*tan(66 deg)*tan(78 deg).

1. tan 6 deg
2. 1
3. sqrt(3)
4. tan 60 deg

Correct answer: tan 6 deg

Solution

Applying tan theta*tan(60-theta)*tan(60+theta) = tan 3 theta repeatedly, the product tan60*tan42*tan66*tan78 collapses to tan6 deg.

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