Решите уравнение 2cos²x-1=0

Question

Решите уравнение 2cos²x-1=0

Answer 1

Cos^2x = 1/2

cosx = - √2/2
x₁ = ± arccos(-√2/2) + 2πn
x₁ = ± (π - π/4) + 2πn
x₁= ± 3π/4 + 2πn, n∈Z

cosx = √2/2
x₂ = ± arccos(√2/2) + 2πk
x₂ = ± π/4 + 2πk, n∈Z