Решите уравнение 2sin^2x-cos2x=1

Question

Решите уравнение 2sin^2x-cos2x=1

Answer 1

2sin^2x - cos2x = 1
2sin^2x - (1 - 2sin^2x) - 1 = 0
2sin^2x - 1 + 2sin^2x - 1 = 0
4sin^2x - 2 = 0
4sin^2x = 2
sin^2x = 1/2
sinx = ± √2/2

1) sinx = √2/2
x = pi/4 + 2pik, k ∈Z
x = 3pi/4+ 2pik, k ∈Z

2) sinx = - √2/2
x = -  pi/4 + 2pik, k ∈ Z
x = 5pi/4 + 2pik, k ∈Z