Use an identity to solve the following equation on the interval [O, 2pi).

cos2x = sin x + 1

x = 0, π, 7π/6, 11π/6

Step-by-step explanation:

cos (2x) = sin x + 1

Use double angle formula.

1 - 2 sin²x = sin x + 1

Move everything to one side.

0 = 2 sin²x + sin x

Factor.

0 = sin x (2 sin x + 1)

Solve.

sin x = 0 or - ½

x = 0, π, 7π/6, 11π/6