Question 308216
Use the cosine angle addition formula.

cos(165°)
= cos(120° + 45°)
= cos(120°)cos(45°) - sin(120°)sin(45°)
= (-1/2)(√2/2) - (√3/2)(√2/2)
= -√2/4 - (√3√2)/4
= -√2/4 - √6/4
= (-√2 - √6)/4

Therefore, cos(165°) = (-√2 - √6)/4.

Hope this helps!