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Find Tan A if Cos2A = 1/2

1 Answer

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Answer:

tan A = ± 1/√3 or ± 0.58

Explanation:

2 ways to solve this question.

1. cos 2A = 1/2 2A = 60° or 300° or 420° or ....

A = 30° or 150° or 210° ....

tan A = tan 30° or tan 150° or ... = ± 1/√3

2. cos 2A = 2 cos²A - 1 1/2 = 2 cos²A - 1 cos²A = 3/4

cos 2A = 1 - 2 sin²A 1/2 = 1 - 2 sin²A sin²A = 1/4

tan²A = sin²a/cos²A = (1/4) / (3/4) = 1/3

tan A = ± 1/√3 or ± 0.58

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