Prove that is an increasing function of θ in

We have, y =

Now,

⟹ 8cosθ + 4 = 4 + cos²θ + 4cosθ

⟹ cos²θ - 4cosθ = 0

⟹ cosθ(cosθ-4) = 0

⟹ cosθ = 0 or cosθ = 4

Since, cosθ≠4, cosθ = 0

⟹ cosθ = 0 ⟹ θ = π/2

Now,

In interval,, we have cos θ > 0. Also, 4 > cos θ

⇒ 4 – cosθ > 0

Therefore, cosθ(4 – cosθ) > 0 and also (2 + cosθ)² > 0

Therefore, y is strictly increasing in interval.

Also, the given function is continuous at x = 0 and x = .

Therefore, y is increasing in interval.