cos(6x)+6cos^2(3x)=1

Вопрос школьника по предмету Алгебра

cos(6x)+6cos^2(3x)=1

Ответ учителя по предмету Алгебра

cos6x + 6cos²3x = 1

cos²3x — sin²3x + 6cos²3x = 1

7cos²3x — sin²3x = 1

7cos²3x — (1 — cos²3x) = 1

7cos²3x — 1 + cos²3x = 1

8cos²3x = 2

4cos²3x = 1

cos²3x = 1/4

cos3x = 1/2

cos3x = -1/2

3x = -π/3 + 2πn

3x = π/3 + 2πn

3x = 2π/3 + 2πn

3x = -2π/3 + 2πn

x = -π/9 + 2πn/3

x = π/9 + 2πn/3

x = 2π/9 + 2πn/3

x = -2π/9 + 2πn/3

OTBET: -π/9 + 2πn/3; π/9 + 2πn/3; -2π/9 + 2πn/3; 2π/9 + 2πn/3; n ∈ Z