Find the exact value of cos 75 degree using the halfangle id

Find the exact value of cos 75 degree using the half-angle identity Choose the exact value of cos 75 degree A. Squareroot 2 + Squareroot 3/2 B. - Squareroot 3/4 c. Squareroot 2 - Squareroot 3/2

Solution

cos 75=cos(150/2)

cos 150=-sqrt3/2

cos75=sqrt(1-costheta)/2) = sqrt((1+sqrt3/2)/2)=sqrt(s+sqrt3)/2