cos (− 7π/12) = ? what did i do wrong? I got Cos(-3pie/12) - Cos(-4pie/12) = -pi/4 - pi/3 =-squrt 2/2 - 1/2 = (-squrt 2 -1) / 2?

The cosine of a sum is NOT the sum of the cosines. You need to use the formula for the cosine of the sum of angles.
.. cos(a+b) = cos(a)cos(b) - sin(a)sin(b)

.. cos(-7π/12) = cos(-3π/12 - 4π/12)
.. = cos(-3π/12)cos(-4π/12) - sin(-3π/12)sin(-4π/12)
.. = cos(π/4)cos(π/3) - sin(π/4)sin(π/3) ... taking odd/even functions into account
.. = (√2)/2*1/2 - (√2)/2*(√3)/2
.. = (√2)/4*(1 - √3)

Cos (− 7π/12) = Cos ( 7π/12) = Cos (π/3+π/4) = cos(a)cos(b)-sin(a)sin(b) = ..