Final answer:
To solve the equation 2cos2x+2cosx=0, we can factor out 2cosx and set each factor equal to zero. This gives us two sets of solutions: x = π/2 + nπ and x = π + nπ, where n is an integer.
Step-by-step explanation:
To solve the equation 2cos2x+2cosx=0, we can factor out 2cosx from both terms:
2cosx(cosx+1)=0
Now we can set each factor equal to zero:
2cosx = 0
cosx + 1 = 0
Solving the first equation, we get cosx = 0. This gives us x = π/2 + nπ, where n is an integer.
Solving the second equation, we get cosx = -1. This gives us x = π + nπ, where n is an integer.