Ну как сдал вчера контрольную? 1/(sin^2 x) + 1/(cos(7pi/2 + x)) = 2 1/(sin^2 x) + 1/(cos(4pi-pi/2+x)) = 2 1/(sin^2 x) + 1/(cos(pi/2-x)) = 2 1/(sin^2 x) + 1/(sin x) = 2 Умножаем всё на sin^2 x 1 + sin x = 2sin^2 x 2sin^2 x - sin x - 1 = 0 (sin x - 1)(2sin x + 1) = 0 sin x = 1; x = -pi/2 + 2pi*k sin x = -1/2; x = -pi/6 + 2pi*n; x = 7pi/6 + 2pi*n
1/(sin^2 x) + 1/(cos(7pi/2 + x)) = 2
1/(sin^2 x) + 1/(cos(4pi-pi/2+x)) = 2
1/(sin^2 x) + 1/(cos(pi/2-x)) = 2
1/(sin^2 x) + 1/(sin x) = 2
Умножаем всё на sin^2 x
1 + sin x = 2sin^2 x
2sin^2 x - sin x - 1 = 0
(sin x - 1)(2sin x + 1) = 0
sin x = 1; x = -pi/2 + 2pi*k
sin x = -1/2; x = -pi/6 + 2pi*n; x = 7pi/6 + 2pi*n
Корни на промежутке [-5pi/2; -pi]: x1 = -5pi/2; x2 = -13pi/6