Final answer:
The exact value of cos 105° is found using the cosine sum formula, resulting in (√2 - √6)/4, making option c the correct answer.
Step-by-step explanation:
The exact value of cos 105° can be found using the sum or difference formulas for cosine. Specifically, we can express 105° as 60° + 45° and use the formula for the cosine of a sum of angles:
cos(105°) = cos(60° + 45°)
cos(105°) = cos(60°)cos(45°) - sin(60°)sin(45°)
cos(60°) = 1/2 and cos(45°) = sin(45°) = √2/2, sin(60°) = √3/2.
Thus,
cos(105°) = (1/2)(√2/2) - (√3/2)(√2/2)
cos(105°) = √2/4 - √6/4
cos(105°) = (√2 - √6)/4
The correct answer is c. √2 - √6/4.