Question

решите уравнение sin 2x - sin x = 2 cos x - 1

Answer 1

sin 2x - sin x = 2cos x - 1

2sin x cos x - sin x = 2cos x - 1

sin x (2cos x - 1) - (2cos x -1) = 0

(2cos x - 1)(sin x - 1) = 0

2cos x - 1 = 0;    x = ±π/3 + 2πn,n ∈ Z

sin x - 1 = 0;     x = π/2 + 2πk,k ∈ Z