Solve the following trigonometric equation on the interval [0, 2π) with the help of an identity.

2sin² x + cos x - 1 = 0

Solve the following trigonometric equation on the interval [0, 2π) with the help of an identity.

sin 2x = 2cos x

Solve the following trigonometric equation on the interval [0, 2π) with the help of an identity.

sin x - cos x = -1

Solve the following trigonometric equation on the interval [0, 2π) with the help of an identity.

tan x - sec x = -1