Recognize that the angle 105° can be expressed as the sum of two angles: 60° and 45°. This allows us to use the angle addition formula for cosine: cos(α + β) = cos(α)cos(β) - sin(α)sin(β).
Substitute α = 60° and β = 45° into the angle addition formula: cos(105°) = cos(60°)cos(45°) - sin(60°)sin(45°).
Recall the exact trigonometric values: cos(60°) = 1/2, cos(45°) = √2/2, sin(60°) = √3/2, and sin(45°) = √2/2.
Substitute these values into the expression: cos(105°) = (1/2)(√2/2) - (√3/2)(√2/2).
Simplify the expression by performing the multiplications and combining the terms: cos(105°) = (√2/4) - (√6/4).