Use the halfangle formulas to find the exact value of the tr

Use the half-angle formulas to find the exact value of the trigonometric function cos 15degree. cos 15degree = (Type an exact answer, using radicals as needed.)

Solution

cos 15=cos(30/2)

cos 3-=sqrt3/2

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

cos(30/2)=sqrt((1 + cos 30)/2)=sqrt((1+ sqrt3/2)/2) = (sqrt(2+sqrt3))/2