Question

Solve cos²x - sin x - 1/4 = 0.

Answer 1

Replacing cos²x by 1 − sin²x, we get a quadratic in sin of the form

4sin²x + 4sinx −3 = 0

⇒ (2sinx + 3) (2sinx −1) = 0

Now

sin x ≠ − 3/2 since |sin x| ≤ 1

Therefore, sin x = 1/2

The principal solution is x = π/6.

The general solution is x = nπ +(-1)ⁿπ/6.