(OCR, C4) Trig/Stationary Points Question

I am having some trouble with Q4 on the June 2013 Paper:

The question:


So dy/dx = -2sin2x + 2cos 2x = 0

Rearanging and using identities gets me
2cos2x = 2 sin2x,
cos2x = sin2x
cos2x= 2sinxcosx
1= 2sin x
1/2 = sin x

so
x= sin^-1 (1/2) = 1/6 pi and 5/6 pi
(and using those values of x, I found the values of y as they are on the mark scheme)

However the mark scheme has an aditonal stationary point with the coordinates, (1/2 pi, 1). I am having trouble figuring out how to get that answer.

Any help would be greatly appreciated!

I am having some trouble with Q4 on the June 2013 Paper:
So dy/dx = -2sin2x + 2cos 2x = 0

Should be 2cos(x) rather than 2cos(2x)

Ah, yes- I made an error when typing out my working (but differentiated right when I did the original question) - im still unable to arrive at the other stationary point

At $cos(x)=2sin(x)cos(x)$ you divided through by cos(x) when you shouldn't do that. By dividing, you are getting rid off one of the solutions, hence the one you are missing. Instead, subtract cos(x) from both sides and factor it out. Then solve two products, each equaling 0.