Для начала найдем sin(α) с помощью тождества tg(α) = sin(α) / cos(α):

tg(α) = sin(α) / cos(α) = -(1/√7)
sin(α) = -(1/√7) * cos(α)

Теперь воспользуемся тождеством cos^2(α) + sin^2(α) = 1:

cos^2(α) + (-1/√7)^2 cos^2(α) = 1
cos^2(α) + 1/7 cos^2(α) = 1
(1 + 1/7) cos^2(α) = 1
8/7 cos^2(α) = 1
cos^2(α) = 7/8
cos(α) = √(7/8) = √7 / 2√2 = √7 / 2√2

Теперь найдем cos(2α):

cos(2α) = cos^2(α) - sin^2(α)
cos(2α) = (7/8) - (1/7) = (49 - 8) / 56 = 41 / 56

Теперь найдем cos(2α - π/2):

cos(2α - π/2) = cos(2α) cos(π/2) + sin(2α) sin(π/2)
cos(2α - π/2) = cos(2α) 0 - sin(2α) 1
cos(2α - π/2) = -sin(2α)

Так как sin(2α) = 2sin(α)cos(α) и sin(α) = -(1/√7), мы можем вычислить sin(2α):

sin(2α) = 2sin(α)cos(α) = 2 -(1/√7) √7 / 2√2 = -1/√2

Таким образом, получаем:

cos(2α - π/2) = -sin(2α) = -(-1/√2) = 1/√2