Question

Помогите с тригонометрией!!!

2cos² x+cos x=0

sin 3x= sin 5x

Answer 1

Объяснение:

1)

2cos²x + cos x = 0

cos x · (2cos x + 1) = 0

cos x = 0 (1) или 2cos x + 1 = 0 (2)

(1)

x = π/2 + πk, k∈Z

(2)

2cos x = -1

cos x = -1/2

x = ±(π - π/3) + 2πn, n∈Z

x = ±2π/3 + 2πn

2)

sin 3x = sin 5x

sin 5x - sin 3x = 0

2 sin ((5x - 3x)/2) · cos ((5x + 3x)/2) = 0

sin x = 0 (1) или cos 4x = 0 (2)

(1)

x = πk, k∈Z

(2)

4x = π/2 + πn, n∈Z

x = π/8 + πn/4