Problem 5 · Cofunction pairing and double-angle identity · 4 points
Made by AI and not reviewed by a real person.
Let A = sin 15° + cos 75° and B = sin 75° + cos 15°. What is A/B + B/A?
- 2 − √3
- 4/√3
- 4
- 2
- 2 + √3
Show a hint
- Look for complementary-angle twins inside each sum before calculating any exact values.
- After simplifying A and B, combine the fractions and use a double-angle identity.
Show the answer and solution
Answer: C — 4
Because 15° and 75° are complementary, A = 2 sin 15° and B = 2 cos 15°. Thus A/B + B/A = (sin² 15° + cos² 15°)/(sin 15° cos 15°) = 1/(sin 15° cos 15°) = 2/sin 30° = 4. The tempting 2 comes from treating A and B as equal, but sin 15° and cos 15° are not equal.