Final answer:
The equation cos(x) = 3cos(x) - 2 simplifies to cos(x) = 1 when rearranged, with the general solution being x = 2nπ, where n is an integer.
Step-by-step explanation:
To solve the equation for cos(x): cos(x) = 3cos(x) - 2, we first need to rearrange the terms to bring all the cos(x) terms to one side of the equation. This gives us:
cos(x) - 3cos(x) + 2 = 0
Simplifying this, we get:
-2cos(x) + 2 = 0
Dividing both sides of the equation by -2 gives us:
cos(x) = 1
The solution to this equation is when the argument of the cosine is an integral multiple of π; specifically, x = 2nπ where n is an integer (since cosine has a period of 2π and cos(0) = 1).