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sin5x+cos5x=1

Введём дополнительный угол.

Посчитаем C = √ (a² + b²)

C = √ (1² + 1²) = √2.

Разделим на √2:

sin5x·√2/2 + cos5x·√2/2 = √2/2

sin (π/4) = cos (π/4) = √2/2

cos5x·cos (π/4) + sin5x·sin (π/4) = √2/2

cos (5x - π/4) = √2/2

5x - π/4 = ±π/4 + 2πn, n ∈ Z

5x = ±π/4 + π/4 + 2πn, n ∈ Z

x = ±π/20 + π/20 + 2πn/5, n ∈ Z

Ответ: x = ±π/20 + π/20 + 2πn/5, n ∈ Z.