Решите уравнение (sqrt(2))/(sin x) + (sqrt(2))/(cos x) = (1)/(sin^2 x) + (1)/(cos^2 x) .

(sqrt(2))/(sin x) + (sqrt(2))/(cos x) = (1)/(sin^2 x) + (1)/(cos^2 x) (1sqrt(2)(sin x + cos x))/(2sin x cos x) = (1)/(4sin^2 x cos^2 x) sin(x + pi/4)sin 2x = 1 [ arrayl cases sin(x + pi/4) = 1 sin 2x = 1 cases cases sin(x + pi/4) = -1 sin 2x = -1 cases array . [ arrayl cases 2x = pi/2 + 2k_1pi x + pi/4 = pi/2 + 2k_2pi cases cases 2x = -pi/2 + 2k_1pi x + pi/4 = -pi/2 + 2k_2pi cases array ., k_1, k_2 in Z [ arrayl cases x = pi/4 + k_1pi x = pi/4 + 2k_2pi cases cases x = -pi/4 + k_1pi x = -3pi/4 + 2k_2pi cases array ., k_1, k_2 in Z [ arrayl x = pi/4 + 2kpi, k in Z x in array . x = pi/4 + 2kpi, k in Z.

x = \pi/4 + 2k\pi,\ k \in \mathbb{Z}