Question

Решите уравнение 4sin³x-s-nx=0

Answer 1

Ответ:

x = πk , k € Z

x = (-1)^k × π/6 + πk , k € Z

x = (-1)^k+1 × π/6 + πk , k € Z

Пошаговое объяснение:

4sin^3x - sinx = 0

Замена sinx = a

4a^3 - a = 0

a(4a^2 - 1) = 0

a1 = 0

4a^2 - 1 = 0

4a^2 = 1

a^2 = 1/4

a2 = 1/2

a3 = -1/2

sinx = 0

x = πk , k € Z

sinx = 1/2

x = (-1)^k × arcsin(1/2) + πk , k € Z

x = (-1)^k × π/6 + πk , k € Z

sinx = -1/2

x = (-1)^k+1 × π/6 + πk , k € Z