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If sec²(theta) = 2 + 2*tan(theta), find tan(theta).

1. 1 + sqrt(2) or 1 - sqrt(2)
2. 1 or -1
3. sqrt(2) or -sqrt(2)
4. 2 or -1

Correct answer: 1 + sqrt(2) or 1 - sqrt(2)

Solution

Substituting sec² = 1 + tan² gives tan²(theta) - 2*tan(theta) - 1 = 0, whose roots are 1 +/- sqrt(2).

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