2022 · Q56
If tan θ + sec θ = 3, then what is the value of 3 tan θ + 9 sec θ?
Elementary MathematicsTrigonometry
- A15
- B17
- C19
- D21
Explanation
With s = secθ, t = tanθ: s+t = 3 and s²-t² = 1 give s-t = 1/3, so s = 5/3, t = 4/3. Then 3tanθ+9secθ = 4+15 = 19. Hence the keyed option is C.