2023 · Q25
What is 3(sin x − cos x)⁴ + 6(sin x + cos x)² + 4(sin⁶x) + 4(cos⁶x) equal to?
Elementary MathematicsTrigonometry
- A9
- B11
- C13
- D15
Explanation
sin^4+cos^4 terms combine: 3(sin-cos)^4+6(sin+cos)^2+4(sin^6+cos^6)=3(1-2s)^2+6(1+2s)+4(1-3s)=13 where s=sin^2 cos^2... evaluates to 13? Option (c).