BRAINLIESTTT ASAP! PLEASE HELP ME :)

0,pi, 7pi/6, 11pi/6

Step-by-step explanation:

Let x = theta

sin x +1 = cos 2x

Subtract cos 2x from each side

sin x +1 - cos 2x = cos 2x- cos 2x

sin x +1 - cos 2x = 0

We know that 1 - cos 2x = 2 sin ^2 x

sin x + 2 sin^2 x = 0

Let y = sin x

y + 2 y^2 =0

Factor out a y

y( 1+2y) =0

Using the zero product property

y=0  1+2y =0

y=0   2y =-1

           y = -1/2

Substituting back in for y

sin x =0          sinx = -1/2

Taking the inverse sin on each side

arcsin sin x = arcsin 0         arcsin sin x = arcsin (-1/2)

x = 0 + 2 pi n                                         x = 7 pi/6 + 2*pi*n

  = pi +2 pi n                                             = 11 pi/6 + 2 pi n

                         where n is an integer

We want solutions between and including 0 to 2pi

0,pi, 7pi/6, 11pi/6