# Prove that

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.

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