Докажите тождество sin(a+π)/sin(a+3π/2) + cos(3π-a)/(cos(π/2+a)-1) - вопрос №7864466323211 от Evangelinaa8 25.01.2021 23:37

Question

Алгебра: Докажите тождество sin(a+π)/sin(a+3π/2) + cos(3π-a)/(cos(π/2+a)-1) = 1/cosa

Evangelinaa8 · Answer

Sin(A + π) = -sinAsin(A + 3π/2) = sin(A + π + π/2) = -sin(A + π/2) = -cosAcos(3π - A) = cos(2π + π - A) = cos(π - A) = -cosAcos(π/2 + A) = -sinA-sinA/(-cosA) - cosA/(-sinA - 1) = sinA/cosA + cosA/(sinA + 1) == [sinA(sinA + 1) + cos²A)]/(sinAcosA + cosA) = (sin²A + cos²A + sinA)/(sinAcosA + cosA) = (1 + sinA)/cos(1 + sinA) = = 1/cosA, чтд ...