Question

If 2 cos² θ + 3 cos θ = 2, then permissible value of cos θ is ________.

Options

• 0

• `1/2`

• 1

• `(- 1)/2`

Answer 1

If 2 cos² θ + 3 cos θ = 2, then permissible value of cos θ is `underline(1/2)`.

Explanation:

We have, 2 cos² θ + 3 cos θ = 2

⇒ 2 cos² θ + 3 cos θ - 2 = 0

⇒ 2 cos² θ + 4 cos θ - cos θ - 2 = 0

⇒ (2 cos θ - 1)(cos θ + 2) = 0

⇒ 2 cos θ - 1 = 0, cos θ + 2 ≠ 0

∴ cos θ = `1/2`