2020 · Q55
If sinθ + cosθ = √2, then what is sin⁶θ + cos⁶θ + 6sin²θcos²θ equal to?
Elementary MathematicsTrigonometry
- A1/4
- B3/4
- C1
- D7/4
Explanation
sin(theta)+cos(theta) = sqrt(2) gives sin(theta)cos(theta) = 1/2. Then sin^6+cos^6 = 1-3*(1/4) = 1/4, and adding 6sin^2cos^2 = 6/4 gives 7/4 total. Hence option (D).