cos(x)=8/9. find cos(x/2)

Question

x is more than zero and less than pi/2

Answer 1

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)