2019 · Q59
What is the value of sin⁶θ + cos⁶θ + 3sin²θcos²θ - 1?
Elementary MathematicsTrigonometry
- A0
- B1
- C2
- D4
Explanation
sin^6 θ + cos^6 θ = (sin^2 θ + cos^2 θ)^3 − 3 sin^2 θ cos^2 θ(sin^2 θ + cos^2 θ) = 1 − 3 sin^2 θ cos^2 θ. Adding 3 sin^2 θ cos^2 θ − 1 gives 0.