Evaluate giving exact values and identities. Calculator based solutions are not acceptable. Thanks for any help

Question

cos (-5pi/12)

Answer 1

That is -75 degrees. Use the formula for cos (A + B), where A = -45 degrees and B = -30 degrees.

cos (-5pi/12) = cos (5pi/12)
= cos45deg*cos30deg - sin45deg*sin30deg
= (sqrt2)/2*(sqrt3)/2 - sqrt2/4
= [(sqrt6)- (sqrt2)]/4
= sqrt2*(sqrt3 -1)/4