Use a halfnumber identity to find an exact value for the fun

Use a half-number identity to find an exact value for the function, given the infromation about x

cos x/2, given cos x =1/4, with 0< x<  /2

Solution

0< x<  /2

=> 0< x/2<  /4

cos x/2 =[(1+cosx)/2] is half angle identity

cos x/2 =[(1+(1/4))/2]

cos x/2 =[(5/4)/2]

cos x/2 =(5/8)