2025 · Q31
If √(2+√(2+√(2+...))) = cosecθ, then what is the value of sinθ?
Elementary MathematicsTrigonometry
- A1
- B√3/2
- C√2/2
- D1/2
Explanation
Let y=sqrt(2+sqrt(2+...)). Then y^2=2+y, so y=2 (y>0). Thus cosec(theta)=2 and sin(theta)=1/2. The fixed-point equation is exact - no need to truncate the radical.