Question

How do you solve the equation 2cos^2 - cosx = 0 for all solutions?

Answer 1

π/2 and π/3

Explanation:

Given the equation 2cos²x - cosx = 0, to find the solution to the equation, we will follow the following step.

let P = cosx

The equation becomes 2P²-P = 0

P(2P-1) = 0

P = 0 and 2P-1 = 0

P= 0 and P = 1/2

Since P = cosx

cosx = 0 and cos(x) = 1/2

If cos(x) = 0

x = cos⁻¹0

x = 90⁰

x = π/2

If cos(x) = 1/2

x = cos⁻¹1/2

x = 60⁰

x = π/3

Hence the solutions to the equation are π/2 and π/3.