Đáp án:

Giải thích các bước giải:

`tan alpha = 3 => cot alpha = 1/3`.

`1 + tan^2 alpha = 1/cos^2 alpha`.

`<=> 1 + 9 = 1/cos^2 alpha => cos^2 alpha = 1/10 =>cos alpha = +-1/sqrt 10`.

Do `alpha in (180, 270) => cos alpha < 0`.

`=> cos alpha = -1/sqrt 10`.

`sin^2 alpha = 1 - 1/10 = 9/10 => sin alpha = -3/sqrt 10`

do `sin alpha < 0` với `alpha in (180, 270)`.

`cos(2alpha + (pi/3)) = cos 2 alpha cos((pi/3)) - sin 2 alpha sin (pi/3).`

`= 1/2 . cos 2 alpha - sqrt 3/2 . sin 2 alpha`.

`= 1/2 . (1 - 2 sin^2 alpha) - sqrt 3/2 . 2 sin alpha cos alpha`.

`= 1/2 . (1 - 2 . 9/10) - sqrt 3/2 . 2 . -3/sqrt 10 . -1/sqrt 10`.

`= 1/2 . (-4/5) - (sqrt 3 . 2 . -3 . -1)/(2.sqrt10.sqrt10)`.

`= -2/5 - (6 sqrt 3)/(20)`

`= (-4- 3 sqrt 3)/10`.