We will use the formula: cos(α + β) = cos(α)cos(β) – sin(α)sin(β)

Cos(30°+45°) = cos(30°)cos(45°) - sin(30°)sin(45°)

Cos(30°+45°) = ((√3)/2)(√2/2) - (1/2)(√2/2)

Cos(30°+45°) = (√6/4) - (√2/4)

Cos(30°+45°) = (1/4)(√6 - √2)