Левая часть уравнения неотрицательна, ⇒
cosx - sinx ≥ 0
√2/2cosx - √2/2sinx ≥ 0
cosx·cos(π/4) - sinx·sin(π/4) ≥ 0
cos(x + π/4) ≥ 0
- π/2 + 2πn ≤ x + π/4 ≤ π/2 + 2πn
- 3π/4 + 2πn ≤ x ≤ π/4 + 2πn
(x + π/2)² ·(cosx - sinx) - π²/4(cosx - sinx) = 0
(cosx - sinx)((x + π/2)² - π²/4) = 0
1) cosx - sinx = 0
√2/2cosx - √2/2sinx = 0
cosx·cos(π/4) - sinx·sin(π/4) = 0
cos(x + π/4) = 0
x + π/4 = π/2 + πk
x = π/4 + πk
2) (x + π/2)² - π²/4 = 0
x² + xπ + π²/4 - π²/4 = 0
x(x + π) = 0
x = 0 x = - π - не входит в ОДЗ
Ответ: x = 0; x = π/4 + πk