Answer: cos 60° = 1/2 and 1-2sin²30° = 1/2 (true).
- A cos 60° = 1/2 and 1-2sin²30° = 1/2 (true)
- B cos 60° = √3/2, mistakenly using the cos 30° value instead
- C They are not equal, since sin²30° was computed as 3/4 in error
- D The identity only works for A = 0, where both sides trivially vanish
Correct answer: A. cos 60° = 1/2 and 1-2sin²30° = 1/2 (true)
Explanation: cos 60° = 1/2. 1 - 2sin²30° = 1 - 2(1/4) = 1/2. Equal. Identity verified.
Unit circle with standard angles 0, 30, 45, 60, 90 degrees; at 45 degrees the point is (cos45, sin45) = (1/sqrt2, 1/sqrt2).
Concept context
Ratios, identities, and applications in triangles