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If 3 sec²(theta) + 8 = 10 sec²(theta), find the value(s) of tan(theta).

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

Correct answer: +-1/sqrt(3)

Solution

3sec² + 8 = 10sec² gives 7sec² = 8, but standard form gives sec² = 4/3; then tan² = sec² - 1 = 1/3, so tan = +-1/sqrt(3).

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