Solve the given equation. (Enter your answers as a comma-separated list. Let k be any integer. Round terms to three decimal places where appropriate. If there is no solution, enter NO SOLUTION.)

Question

2 sin²(𝜃) − cos(𝜃) = 1

How can this be solved?

Answer 1

Since cos²θ + sin²θ = 1, sin²θ = 1 - cos²θ

So, the given equation is equivalent to 2(1 - cos²θ) - cosθ = 1

-2cos²θ - cosθ + 1 = 0

2cos²θ + cosθ - 1 = 0

(2cosθ - 1)(cosθ + 1) = 0

cosθ = 1/2 or cosθ = -1

cosθ = 1/2 when θ = π/3 + 2kπ or 5π/3 + 2kπ

cosθ = -1 when θ = π + 2kπ