Решите уравнение, упростив левую часть: 1) 4sin x cos x = 1 2) 4sin^2 2x - cos^2 2x = корень из 3 /2 3) sinx * cos 2x + sin 2x * cosx = 0 Пожалуйста, развернутый ответ
1) 4sin x*cos x = 2sin 2x = 1 sin 2x = 1/2 2x = pi/6 + 2pi*k; x1 = pi/12 + pi*k 2x = 5pi/6 + 2pi*k; x2 = 5pi/12 + pi*k 2) 4sin^2 2x - cos^2 2x = 1/2*(8sin^2 2x - 2cos^2 2x) = = 1/2*(3sin^2 2x + 5sin^2 2x + 5cos^2 2x - 3cos^2 2x) = = 1/2*(5(sin^2 2x + cos^2 2x) - 3(cos^2 2x - sin^2 2x) = = 1/2*(5 - 3cos 4x) = √3/2 5 - 3cos 4x = √3 cos 4x = (5 - √3)/3 4x = +- arccos ((5 - √3)/3) + 2pi*k x = +- 1/4*arccos ((5 - √3)/3) + pi*k/2 3) sin x*cos 2x + sin 2x*cos x = sin x*(2cos^2 x - 1) + 2sin x*cos x*cos x = = 2sin x*cos^2 x - sin x + 2sin x*cos^2 x = sin x*(4cos^2 x - 1) = = sin x*(2cos x - 1)(2cos x + 1) = 0 sin x = 0; x1 = pi*k cos x = -1/2; x2 = 2pi/3 + 2pi*n; x3 = 4pi/3 + 2pi*n cos x = 1/2; x4 = pi/3 + 2pi*m; x5 = -pi/3 + 2pi*m