Using sum or difference formulas find the exact value of cos

Using sum or difference formulas, find the exact value of cos(105). Express your answer in the form cos(105)=(sqrt(a)(1-sqrt(b)))/4 for some numbers a and b

Solution

cos(105) = cos(60 + 45)

= cos60cos45 - sin60sin45

= (1/2)(1/sqrt(2)) - (sqrt(3)/2)(1/sqrt(2))

= (1 - sqrt(3))(1/2sqrt(2))

= (sqrt(2)(1-sqrt(3)))/4

a = 2, b = 3