Answer: π/4.
- A π/4
- B π/2
- C π/3
- D π
Correct answer: A. π/4
Explanation: tan(2β): sin β = 1/√10, cos β = 3/√10. tan β = 1/3. tan(2β) = 2(1/3)/(1-1/9) = (2/3)/(8/9) = 3/4. tan(α+2β) = (1/7 + 3/4)/(1 - 3/28) = (25/28)/(25/28) = 1. So α+2β = π/4.
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