Answer: 1/2.
- A 1/2
- B 1
- C √5/2
- D (√5-1)/2
Correct answer: A. 1/2
Explanation: Exact values from pentagon: cos36°=(1+√5)/4 and cos72°=(√5−1)/4. Difference=(1+√5)/4−(√5−1)/4=(1+√5−√5+1)/4=2/4=1/2. Verify: cos36°≈0.809, cos72°≈0.309, diff≈0.5 ✓.
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