Решите уравнение sin19x/2+cos19x/2=1

sin (19 * x/2) + cos (19 * x/2) = 1;

Возведем уравнение в квадрат.

(sin (19 * x/2) + cos (19 * x/2)) ^2 = 1^2;

sin^2 (19 * x/2) + 2 * sin (19 * x/2) * cos (19 * x/2) + cos^2 (19 * x/2) = 1;

sin (2 * (19 * x/2)) + (sin^2 (19 * x/2) + cos^2 (19 * x/2)) = 1;

sin (2 * 19 * x/2) + 1 = 1;

sin (19 * x) + 1 = 1;

sin (19 * x) = 1 - 1;

sin (19 * x) = 0;

19 * x = пи * n, n ∈ Z;

x = пи/19 * n, n ∈ Z.

Ответ: x = пи/19 * n, n ∈ Z.