Find the exact value of Cos(-pi/12)
You did ask for the EXACT value, which no one has posted yet. The exact value is √(2 + √3)/2. To three decimal places, that is .966.
As for how I got that, I started with a 30-60-90 triangle and extended the longer side by the length of the hypotenuse to get a 15-75-90 triangle, then used Pythagoragus. For some reason, though, most students have an easier time using a half-angle formula, so feel free to do it that way.
OK, sorry, I see Awesome Sauce also gives an exact value. It is also correct, just looks a little different.
From your comment in Additional Details, it appears you want to use the angle difference relation: cos(π/12) = cos(π/4 - π/6). That works also, but you need to get the formula right, which is:
cos(a - b) = cos a cos b + sin a sin b
For cos (45 - 30), this gives cos 45 cos 30 + sin 45 sin 30 = √2/2 √3/2 + √2/2 1/2 = √2/4(√3 + 1). This is yet another expression for the same exact value.