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Given sec(theta) = 5/4, find tan(theta/2) and tan(theta).

1. tan(theta/2) = 1/3, tan(theta) = 3/4
2. tan(theta/2) = 1/2, tan(theta) = 4/3
3. tan(theta/2) = 3/4, tan(theta) = 1/3
4. tan(theta/2) = 1/3, tan(theta) = 4/3

Correct answer: tan(theta/2) = 1/3, tan(theta) = 3/4

Solution

With cos = 4/5 and sin = 3/5, tan(theta) = 3/4 and tan(theta/2) = (3/5)/(1 + 4/5) = 1/3.

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