2022 · Q49
If cosθ + secθ - 2 = 0, where 0 ≤ θ < (π)/(2), then what is the value of cos⁴θ + sec⁴θ - 2?
Elementary MathematicsTrigonometry
- A-2
- B-1
- C0
- D2
Explanation
cosθ+secθ = 2 multiplies to (cosθ-1)² = 0, so cosθ = 1 (θ = 0). Then cos⁴θ+sec⁴θ-2 = 1+1-2 = 0. Hence the keyed option is C.