Question

Solve cos²(x) - cos(x) = 0 for x, 0 <= x <= 2π. (select all that apply.)

A. 2π
B. π/2
C. 0
D. 3π/2
E. π

Answer 1

To solve the equation cos²(x) - cos(x) = 0 for x, 0 ≤ x ≤ 2π, factor out the common term cos(x) to get cos(x)(cos(x) - 1) = 0. The possible values of x that satisfy this equation are x = π/2, x = 3π/2, and x = 2π.

Step-by-step explanation:

To solve the equation cos²(x) - cos(x) = 0 for x in the interval 0 ≤ x ≤ 2π, we can factor out the common term cos(x) to get cos(x)(cos(x) - 1) = 0. This equation will be true when either cos(x) = 0 or cos(x) - 1 = 0. So the possible values of x are the solutions to these equations, which are:

1. x = π/2
2. x = 3π/2
3. x = 2π