Answer:
cos(theta/2) = sqrt((1+x)/2)
Step-by-step explanation:
From the double angle formula
cos^2(t)-sin^2(t) = cos(2t) ...................(1)
cos^2(x)+sin^2(x) = cos(t-t) =1...............(2)
Add (1) and (2)
2cos^2(t) = 1+cos(2t)
cos^2(t) = (1+cos(2t))/2
cos(t) = sqrt((1+cos(2t))/2)
substitute t = theta/2
cos(theta/2) = sqrt((1+cos(theta))/2)
substitute cos(theta) = x
cos(theta/2) = sqrt((1+x)/2)
