Use the half angle formulas to find the exact value of the t

Use the half angle formulas to find the exact value of the treignometric function cos (-15 degrees)

If you can show the steps clearly it will be greatly appreciated. Thank you in advance.

Solution

cos( -15) =cos15

cos2x = 2cos^2x -1

x = 15

cos15 = sqrt{( 1 +cos30)/2}

we lknow cos30 = sqrt3/2

so,cos15 = sqrt{ ( 1+sqrt3/2)/2 }

= sqrt{ ( 2+ sqrt3)}/2