Решить систему sin x+sin y=1/2, sin x*sin y=-1/2 - вопрос №12127309167 от Sasha77999 17.08.2022 06:55

Question

Алгебра: Решить систему sin x+sin y=1/2, sin x*sin y=-1/2

Sasha77999 · Answer

Sinx + siny = 1/2sinx * siny = -1/2sinx = 1/2 - siny(1/2 - siny)*siny = -1/2sinx = 1/2 - siny1/2siny - sin²y + 1/2 = 0siny = t1/2t - t² + 1/2 = 0t² - 1/2t - 1/2 = 02t² - t - 1 = 0t = 1t = -1/2siny = 1siny = -1/2sinx₁ = 1/2 - siny₁siny₁ = 1sinx₁ = -1/2siny₁ = 1x₁ = -π/6 + 2πnx₂ = -5π/6 + 2πny₁ = π/2 + 2πnsinx₃ = 1/2 - siny₂siny₂ = -1/2sinx₃ = 1siny₂ = -1/2x₃ = π/2 + 2πny₂ = -π/6 + 2πny₃ = -5π/6 + 2πnответ: (π/2 + 2πn; -π/6 + 2πn); (π/2 + 2πn; -5π/6 + 2πn); (-π/6 + 2πn; π/2 + 2πn); (-5π/6 + 2πn; π/2...