sin (180/6+x) - sin (180/6-x) = 1

Воспользуемся формулой:

sina - sinb = 2sin ((a - b) / 2) * cos ((a + b) / 2); sin (180°/6 + x) - sin (180°/6 - x) = 1; sin (30° + x) - sin (30° - x) = 1; 2sin{ ((30° + x) - (30° - x)) / 2} * cos{ ((30° + x) + (30° - x)) / 2} = 1; 2sin{ (30° + x - 30° + x) / 2} * cos{ (30° + x + 30° - x) / 2} = 1; 2sin (2x/2) * cos (60°/2) = 1; 2sinx * cos30° = 1; 2sinx * √3/2 = 1; sinx * √3 = 1; sinx = 1/√3 = √3/3; [x = arcsin (√3/3) + 2πk, k ∈ Z;

[x = π - arcsin (√3/3) + 2πk, k ∈ Z.

Ответ: arcsin (√3/3) + 2πk; π - arcsin (√3/3) + 2πk, k ∈ Z.