Đáp án:

`text{C. } 2 cos alpha`

Hướng dẫn cách làm:

`text{A} = (1 + cos alpha + cos 2alpha + cos 3alpha) / (2 cos^2 alpha + cos alpha - 1)`

`= ((1 + cos 2alpha) + (cos alpha + cos 3alpha)) / (2 cos^2 alpha + cos alpha - 1)`

`= (2 cos^2 alpha + 2 cos 2alpha cos alpha) / (2 cos^2 alpha + cos alpha - 1)`

`= (2 cos^2 alpha + 2 (2 cos^2 alpha - 1) cos alpha) / (2 cos^2 alpha + cos alpha - 1)`

`= (2 cos^2 alpha + 4 cos^3 alpha - 2 cos alpha) / (2 cos^2 alpha + cos alpha - 1)`

`= (2 cos alpha (2 cos^2 alpha + cos alpha - 1)) / (2 cos^2 alpha + cos alpha - 1)`

`= 2 cos alpha`

Vậy `text{A} =2 cos alpha`

$\longrightarrow$ Chọn `text{C. } 2 cos alpha`