Cos (x) + sqrt ((2-sqrt2) / 2 * (sinx+1)) = 0

Сos (x) + √ ((2-√2) / 2 * (sin (x) + 1)) = 0

сos (x) = - √ ((2-√2) / 2 * (sin (x) + 1))

√ (1-sin² (x)) = - √ ((1-√2/2) * (sin (x) + 1))

1-sin² (x) = (1-√2/2) * (sin (x) + 1)

1-sin² (x) = 1-√2/2 + sin (x) - √2/2*sin (x)

sin² (x) + sin (x) - √2/2*sin (x) - √2/2=0

sin (x) * (sin (x) + 1) - √2/2 * (sin (x) + 1) = 0

(sin (x) - √2/2) * (sin (x) + 1) = 0

1. sin (x) - √2/2=0

sin (x) = √2/2

Проверка:

√2/2+√ ((2-√2) / 2 * (√2/2+1)) = 0

√2/2+√ ((1-√2/2) * (√2/2+1)) = 0

√2/2+1-√2/2=0

1≠0

Посторонний корень.

2. sin (x) + 1=0

sin (x) = - 1

Проверка:

0+√ ((2-√2) / 2 * (-1+1)) = 0

√0=0

Корень является решением данного уравнения

х=arcsin (-1) + 2*π*n

x = (3π) / 2+2πn

Ответ: x = (3π) / 2+2πn