Use an appropriate hairangle formula to find the exact value

Use an appropriate hair-angle formula to find the exact value COs(15 pi/8). Show your work. Find the exact value of the given expression: sin (1/2 cos^-1 (12/13))

Solution

cos (15pi/8)=cos(15pi/4/2)

cos (15pi/4)=1/sqrt 2

cos (a/2)=sqrt((1+cos a)/2)

cos(15pi/8)=sqrt((1+cos(15pi/4)/2)=sqrt((sqrt2 +1)/2sqrt2)