Решите уравнение: 2 cos (п/4 - x/2) = 1

2 cos (п/4 - x/2) = 1;
2 sin(п/4 + x/2) = 1;
sin(п/4 + x/2) = 1/2;
п/4 + x/2 =(-1)^k arc sin(1/2) + пk, kZ
1)п/4 + x/2 = 2пk + п/6;
x/2 = 2пk - п/4 + п/6 = 2пk - п/12;
x = 4пk - п/6;
2)п/4 + x/2 = 2пk + 5п/6;
x/2 =2пk - п/4 + 5п/6 = 2пk + 7п/12;
x = 4пk + 7п/6; kZ
Ответ: x = 4пk - п/6; x = 4пk + 7п/6, kZ.