Решите уравнение 2sin^2x=cosx+1

Question

Решите уравнение 2sin^2x=cosx+1

Answer 1

2sin^2x = cosx + 1

2 * (1 - cos^2x) = cosx + 1

2 - 2cos^2x = cosx + 1

2cox^2x + cosx - 1 = 0

D = 1 + 8 = 9

cosx = (-1 + 3)/4 = 1/2

cosx = (-1-3)/4 = -1

x = +- π/3 + 2πk, k ∈ Z

x = π + 2πn, n ∈ Z

Comments

Спасибо большое