The solution of the equation cos² θ + sin θ + 1 = 0 lies between:

The solution of the equation cos² θ + sin θ + 1 = 0 lies…

The solution of the equation cos² ${{\theta}}$ + sin ${{\theta}}$ + 1 = 0 lies between:

Show answer & explanation

Correct answer: B

Explanation

The correct answer is Option 2 i.e. $({{5π} \over 4},{{7π} \over 4})$ .

cos²θ + sinθ + 1 = 0

⇒ 1 - sin²θ + sinθ + 1 = 0

⇒ sin²θ - sinθ - 2 = 0

⇒ (sinθ + 1)(sinθ - 2) = 0

⇒ sinθ = -1 = sin(3π/2)

⇒ θ = (3π/2) = (6π/4) ∈ $({{5π} \over 4},{{7π} \over 4})$