Question

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

a.x=0
b.x=π/2
c.x=π
d.None

Answer 1

The solutions to the equation cos^2(x) - cos(x) = 0 are x = π/2 and x = 0. The correct option is a and b.

Step-by-step explanation:

To solve the equation cos^2(x) - cos(x) = 0, we can factor out a common term of cos(x):

cos(x)(cos(x) - 1) = 0

Now we set each factor equal to zero and solve for x:

cos(x) = 0 or cos(x) - 1 = 0

For the first equation, cos(x) = 0, we know that cos(x) = 0 when x = π/2.

For the second equation, cos(x) - 1 = 0, we can add 1 to both sides to get cos(x) = 1.

The cosine function is equal to 1 when x = 0.

Therefore, the solutions to the equation cos^2(x) - cos(x) = 0 are x = π/2 and x = 0.