cos(180+60) = cos(240) = cos(180)cos(60) - sin(180)sin(60)

cos(180) = -1
sin(180) = 0
cos(60) = 0.5
sin(60) = √3/2

Therefore,
cos(180+60) = -10.5 - 0√3/2 = -0.5

cos(90+60) = cos(150) = cos(90)cos(60) - sin(90)sin(60)

cos(90) = 0
sin(90) = 1

Therefore,
cos(90+60) = 00.5 - 1√3/2 = -√3/2

Therefore,
cos(180+60) - cos(90+60) = -0.5 - (-√3/2)
= -0.5 + √3/2
= (√3 - 1)/2 ≈ 0.366025.

Therefore, the value of cos(180+60) - cos(90+60) is approximately 0.366025.