Решите тригонометрические уравнения. Хотя бы одно!

cos (7X) - cos (X) - sin (4X) = 0

sin^2 (X) + 6cos^2 (X) + 7sin (X) cos (X) = 0

4sin^2 (X) + 5sin (X) cos (X) - cos^2 (X) = 2

sin (2X) + корень из 2 * sin (x-п/4) = 1

1) cos (7X) - cos (X) - sin (4X) = 0

-Sin4xCos3x - Sin4x = 0

-Sin4x (Cos3x + 1) = 0

Sin4x = 0 Cos3x + 1 = 0

4x = πn, n ∈ Z Cos3x = - 1

x = πn/4, n ∈Z 3x = π + πk, k ∈ Z

x = π/3 + πk/3, k ∈Z

2) sin^2 (X) + 6cos^2 (X) + 7sin (X) cos (X) = 0 | : Cos ²x≠0

tg²x + 6 + 7tgx = 0

tg²x + 7tgx + 6 = 0

по т. виета корни - 1 и - 6

tgx = - 1 tgx = - 6

x = - π/4 + πk, k ∈ Z x = arctg (-6) + πn, n ∈Z

3) 4sin^2 (X) + 5sin (X) cos (X) - cos^2 (X) = 2*1

4sin^2 (X) + 5sin (X) cos (X) - cos^2 (X) = 2 * (sin²x + cos²x)

4Sin ²x + 5SinxCosx - Cos²x - 2Sin²x - 2Cos²x = 0

2Sin ²x + 5sinxCosx - 3Cos²x = 0 | : Cos²x≠0

2tg ²x + 5tgx - 3 = 0

tgx = 1/2 tgx = - 3

x = arctg (1/2) + πk, k ∈Z x = - arctg3 + πn, n ∈ Z

sin (2X) + корень из 2 * sin (x-п/4) = 1