To solve the equation cos(3x) - cos(7x) = 0, we can use the trigonometric identity:

cos(a) - cos(b) = -2sin((a+b)/2)sin((a-b)/2)

Applying this identity to the equation, we have:

-2sin((3x+7x)/2)sin((3x-7x)/2) = 0

Simplifying further:

-2sin(5x/2)sin(-2x/2) = 0

sin(5x/2)sin(x) = 0

Now, we have two cases to consider:

Case 1: sin(5x/2) = 0
This occurs when 5x/2 = nπ, where n is an integer.
Solving for x, we have:
5x/2 = nπ
x = (2nπ)/5

Case 2: sin(x) = 0
This occurs when x = nπ, where n is an integer.

Therefore, the solutions to the equation cos(3x) - cos(7x) = 0 are:
x = (2nπ)/5 and x = nπ, where n is an integer.