cos(x)=8/9. find cos(x/2) .
A trig identity is cos(2x) = cos^2(x) - sin^2(x) = 2cos^2(x) - 1 = 1 - 2sin^2(x).
using cos(2x) = 2cos^2(x) - 1
then cos(x) = 2cos^2(x/2) - 1
So, 8/9 = 2cos^2(x/2) - 1
2cos^2(x/2) = 8/9 + 1 = 17/9
cos^2(x/2) = 17/18
cos(x/2) = sqrt(17/18)