2021 · Q48
If 6 + 8 tan θ = sec θ and 8 − 6 tan θ = k sec θ, then what is the value of k²?
Elementary MathematicsTrigonometry
- A11
- B22
- C77
- D99
Explanation
Squaring and adding the two equations: (6+8tanθ)² + (8−6tanθ)² = 100 + 100tan²θ = 100sec²θ. The right sides give sec²θ + k²sec²θ = sec²θ(1+k²). Hence 1 + k² = 100 and k² = 99. Hence option D.