First, split the angle into two angles where the values of the six trigonometric functions are known. In this case, 105, can be split into 45+60 (cos (45+60))
Use the sum formula for cosine to simplify the expression. The formula states that cos (A+B) = - (cos (A) cos (B) + sin (A) sin (B)).
The exact value of cos(60) is 1/2. So multiply 1/2 to cos (45) - sin (60) times sin (45).
The exact value of cos (45) is the square root of 2 over 2