17π/12=7π/4-π/3

Use the sum and difference formula.

cos(17π/12)=cos(7π/4-π/3)

=cos(7π/4)cos(π/3)+sin(7π/4)sin(π/3)

=(√2/2)(1/2)+(-√2/2)(√3/2)

=(1/2√2)+(-√3/2√2)

={(1-√3)/2√2}