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If tan²(theta) + sec(theta) = 5, find the possible value(s) of cos(theta).

1. cos(theta) = 1/2 or cos(theta) = -1/3
2. cos(theta) = 1/3 or cos(theta) = -1/2
3. cos(theta) = 1/4 or cos(theta) = -1/3
4. cos(theta) = 1/2 only

Correct answer: cos(theta) = 1/2 or cos(theta) = -1/3

Solution

Using tan² = sec² - 1 gives sec² + sec - 6 = 0, so sec = 2 or sec = -3, i.e. cos = 1/2 or cos = -1/3.

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