Помогите пожалуйста!!! Тригонометрические уравнения: 1) 2sinx+1=0 2) tg(3x-π)=0 3) 2cosx+√3=0 4) 2sin2x=√3 5) sinx-√3 cosx=0 6) tg2x=1 7) 2sinx=1 8) 8sin^2 x-10sin x-7=0 9) 4sin 2x+10cos2x=1

1) 2 sin x + 1 = 0 2 sin x = -1 sin x = -1/2 x = (-1) ^ n * (- п/6) + пn 2) tg (3x - п) = 0 3x - п = пn 3x = пn + п х = пn/3 + п/3 3) 2 cos x + √3 = 0 2 cos x = - √3 Cos x = - √3/2 X = ±5π/6 + 2πn 4) 2 sin 2x = √3 Sin 2x = √3 / 2 2X = (-1)^n * π/3 + πn X = (-1)^n * π/6 + πn/2 5) sin x - √3 cos x = 0 2 sin (x- π/3) = 0 Sin (x - π/3) = 0 X - π/3 = πn X = π/3+ πn 6) tg 2x = 1 2x = π/4 + πn X = π/8 + πn/2 7) 2 sin x = 1 Sin x = ½ X = (-1)^n * π/6 + πn 8) 8 sin ^ 2 x – 10 sin x – 7 =0 Замена sin x = t, -1 ≤ t ≤ 1 8 t^2 – 10 t – 7 =0 D = 100+7*8*4 = 324 T1 = (10 + 18) / 16 = 28/ 16 = 7/4 – не удовлетворяет условию замены T2 = (10 - 18) / 16 = -8 / 16 = -1/2 Обратная замена: Sin x = -1/2 X = (-1)^n *(-π/6) + πn 9)4 sin 2x + 10 cos 2x = 1 2 √29 sin (2x +arctg 5/2) = 1 sin (2x +arctg 5/2) = 1 / 2 √29 2x +arctg 5/2 = (-1) ^n * arcsin (1 / 2 √29) + πn 2x = (-1) ^n * arcsin (1 / 2 √29) + πn - arctg 5/2 X = (-1) ^n * arcsin (1 / 2 √29)/2 + πn/2 – (arctg 5/2) / 2