use a sum or difference formula to find the exact of the trigonometric function

Question

cos(-13pi/12)

Answer 1

cos(-13pi/12)
= cos(-13pi/12 + 24pi/12)
= cos(11pi/12)
= -cos(pi - 11pi/12)
= -cos(pi/12)

now, cos(x/2) = √((1+cos(x))/2)

-cos(pi/12) = -√((1+cos(pi/6))/2)
= -√((1+√3/2)/2)
= -√(2 + √3/4)
= -1/2 √(2+√3)

or
-1/2√2 (1+√3)