Not sure how you got your answer...
I've used the sum and difference identity for cos and here is my answer:
Cos -5pi/12 I translate as -75 degrees, so I used my known angles which were:
pi/-6 and -pi/4.
I also know that -5pi/12 is in the 4th region so the value should be positive (All Students Take Calculus).
From the Cosine Sum formula we have:
Cos(-pi/4 + -pi/6)= Cos(-pi/4)Cos(-pi/6)-Sin(-pi/4)Sin(-pi/6)
Cos(-pi/4 + -pi/6)=(sqrt2/2)(sqrt3/2)-(sqrt2/2)(1/2)
So what Did I do wrong guys?