Start by the identity \(\cos\left(\frac{x}{2}\right)=\pm\sqrt{\frac{1+\cos x}{2}}\)

I'm assuming the range of \(x\) in this problem is in the range of \(0 (Sorry if this is the wrong range, I assumed this range because for problems normally like this thats the range they use.)

Notice that this range can also be \(0<\frac{x}{2}<\frac{\pi}{4}.\)

Since \(\cos\) is positive here, we use \(\sqrt{\frac{1+\cos x}{2}}\)

Since \(x=-\frac{2}{3}\) , then \(\sqrt{\frac{1-2/3}{2}}.\)

I will leave the radical simplification to you. If you need further help, contact me .