Дано уравнение:
5sin(α) + 4cos(α) -2 / 5sin(α) + 2cos(α) -6 = 1/3
Перепишем это уравнение, используя тригонометрические тождества:
(5sin(α) + 4cos(α)) / (5sin(α) + 2cos(α)) - 6 = 1/3(5sin(α) / 5sin(α)) + (4cos(α) / 5sin(α)) + (2cos(α) / 5sin(α)) - 6 = 1/31 + (4cos(α) / 5sin(α)) + (2cos(α) / 5sin(α)) - 6 = 1/3(4cos(α) + 2cos(α)) / 5sin(α) - 5 = 1/3(6cos(α)) / 5sin(α) = 1/3 + 5(6cos(α)) / 5sin(α) = 16/3
Теперь выразим tg(α):
tg(α) = sin(α) / cos(α) = (1 / cos(α)) / (1 / sin(α)) = 1 / cos(α) sin(α)tg(α) = 1 / ((6 / 5) sin(α)) = 5 / (6 sin(α)) = 5 / (6 √(1 - cos^2(α)))
Таким образом получаем tg(α) = 5 / (6 * √(1 - cos^2(α))).
Дано уравнение:
5sin(α) + 4cos(α) -2 / 5sin(α) + 2cos(α) -6 = 1/3
Перепишем это уравнение, используя тригонометрические тождества:
(5sin(α) + 4cos(α)) / (5sin(α) + 2cos(α)) - 6 = 1/3
(5sin(α) / 5sin(α)) + (4cos(α) / 5sin(α)) + (2cos(α) / 5sin(α)) - 6 = 1/3
1 + (4cos(α) / 5sin(α)) + (2cos(α) / 5sin(α)) - 6 = 1/3
(4cos(α) + 2cos(α)) / 5sin(α) - 5 = 1/3
(6cos(α)) / 5sin(α) = 1/3 + 5
(6cos(α)) / 5sin(α) = 16/3
Теперь выразим tg(α):
tg(α) = sin(α) / cos(α) = (1 / cos(α)) / (1 / sin(α)) = 1 / cos(α) sin(α)
tg(α) = 1 / ((6 / 5) sin(α)) = 5 / (6 sin(α)) = 5 / (6 √(1 - cos^2(α)))
Таким образом получаем tg(α) = 5 / (6 * √(1 - cos^2(α))).