Ответ:

1/2, или 0,5

Пошаговое объяснение:

(sin(α)cos(30°) - cos(α) sin(30°))^2+(sin(30°)cos(α)+cos(30°)sin(α))^2-sin(α)^2

(sin(α) * √3/2 - cos(α)* 1/2) ^2+ (1/2*cos(α)+√3/2*sin(α))^2-sin(α)^2

(√3sin(α)/2 - cos (α)/2)^2 + (cos(α)/2+√3 sin (α)/2) ^2 - sin (α)^2

(√3sin(α)- cos (α)/2)^2 + (cos(α)+√3sin(α)/2) ^2 -sin(α)^2

(√3sin(α)-cos(α))^2 / 4 +(cos(α)+√3sin(α))^2 / 4 - sin(α)^2
3sin(α)-2√3sin(α)cos(α)+cos(α)^2 / 4 + cos(α)^2+2√3cos(α)sin(α)+3sin(α)^2 / 4 - sin(α)^2
2sin(α)^2+sin(α)^2- 2√3sin(α)cos(α)+cos(α)^2 /4 + cos(α)^2+2√3cos(α)sin(α)+2sin(α)^2+sin(α)^2 / 4 - sin(α)^2
2sin(α)^2+1-sin(2a)*√3 / 4 + 1+sin(2α)*√3+2sin(α)^2 / 4 - sin(α)^2
2sin(α)^2+1-√3 sin(2α) / 4 + 1+√3 sin(2α)+2sin(α)^2 / 4 - sin(α)^2
2sin(α)^2+1-√3sin(2α)+1+√3 sin(2α)+2sin(α)^2-4sin(α)^2 / 4
0+2 / 4
2/4
1/2