2018 · Q54
What is sin⁴θ - cos⁴θ equal to for any real number θ?
Elementary MathematicsTrigonometry
- A1
- B1 - 2sin²θ
- C2cos²θ + 1
- D1 - 2cos²θ
Explanation
Factor as a difference of squares: sin⁴θ − cos⁴θ = (sin²θ − cos²θ)(sin²θ + cos²θ) = sin²θ − cos²θ = 1 − 2cos²θ, option (D). Option (B) is the sign-flipped trap.