cos(x+20)-cos(x+80)=0.5

Solution for cos(x+20)-cos(x+80)=0.5 equation:

Simplifying
cos(x + 20) + -1cos(x + 80) = 0.5

Reorder the terms:
cos(20 + x) + -1cos(x + 80) = 0.5
(20 * cos + x * cos) + -1cos(x + 80) = 0.5
(20cos + cosx) + -1cos(x + 80) = 0.5

Reorder the terms:
20cos + cosx + -1cos(80 + x) = 0.5
20cos + cosx + (80 * -1cos + x * -1cos) = 0.5
20cos + cosx + (-80cos + -1cosx) = 0.5

Reorder the terms:
20cos + -80cos + cosx + -1cosx = 0.5

Combine like terms: 20cos + -80cos = -60cos
-60cos + cosx + -1cosx = 0.5

Combine like terms: cosx + -1cosx = 0
-60cos + 0 = 0.5
-60cos = 0.5

Solving
-60cos = 0.5

Solving for variable 'c'.

Move all terms containing c to the left, all other terms to the right.

Divide each side by '-60os'.
c = -0.008333333333o-1s-1

Simplifying
c = -0.008333333333o-1s-1