What is the exact value of cos 105 degrees?

Your answer is C c:

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 

(1/2) ⋅ (√2/2) - sin (60) ⋅ sin (45)

Value of sin (60) is √3/2

(1/2) ⋅ (√2/2) - √3/2 ⋅ sin (45)

exact value of sin (45) is √2/2

(1/2) ⋅ (√2/2) - √3/2 ⋅ √2/2 

all that equals √2/4 - √6/4