2cos^2x=cosx. Can you subtract the cos from cos^2? Or what would i have to do?

To solve the equation 2cos^2x = cosx, you need to rewrite the equation in a form where one side is equal to zero. Here's how you can solve it step by step:

1. Move all terms to the left side to form a quadratic equation. Subtract cosx from both sides:
2cos^2x - cosx = 0

2. Factor out the common term cosx from both terms on the left side:
cosx(2cosx - 1) = 0

3. Now, set each factor equal to zero and solve for x individually:
cosx = 0 (Equation 1)
or
2cosx - 1 = 0 (Equation 2)

To solve Equation 1:
To find the solutions to cosx = 0, you can recall the unit circle or use the knowledge that cosx = 0 when x is equal to odd multiples of π/2 or (2n + 1)π/2, where n is any integer. So the solutions for Equation 1 are:
x = π/2 + nπ (where n is any integer)

To solve Equation 2:
Move the constant term to the right side of the equation:
2cosx = 1
Divide both sides of the equation by 2:
cosx = 1/2

To find the solutions to cosx = 1/2, you can again recall the unit circle or use trigonometric identities. One way to find the solutions is by consulting the special angles for cosine. For cosx = 1/2, the solutions lie at x = π/3 + 2πn or x = 5π/3 + 2πn, where n is any integer.

So, the final solution set for the given equation 2cos^2x = cosx is:
x = π/2 + nπ or x = π/3 + 2πn or x = 5π/3 + 2πn (where n is any integer).