sin x\3 cos П\5 - cos x\3 sin П\5 =√2\2

Ответ:

Пошаговое объяснение:

1) sinx/3cosπ/5 - cosx/3sinπ/5 = √2/2;   sin(x/3 - π/5) = √2/2;   a) x/3 - π/5 = π/4 + 2πk, k ∈ Z;  x/3 = π/5 + π/4 + 2πk, k ∈ Z;  x/3 = 9π/20 + 2πk, k ∈ Z,        x = 27π/20 + 6πk, k ∈ Z;   b) x/3 - π/5 = (π - π/4) + 2πn, n ∈ Z;  x/3 = π/5 + 3π/4 + 2πn , n ∈ Z;  x/3 = 19π/20 + 2πn, n ∈ Z;  x = 57π/20 + 6πn, n ∈ Z;           Ответ: x = 27π/20 + 6πk, k ∈ Z;    x = 57π/20 + 6πn, n ∈ Z;