If $3 \sec \theta+4 \cos \theta-4 \sqrt{3}=0$ where $\theta$ is an acute angle then the value of $\theta$ is:

30°

3 secθ + 4 cosθ - 4√3 = 0

3 × \(\frac{1}{cosθ}\) + 4 cosθ - 4√3 = 0

4 cos²θ - 4√3cosθ  + 3= 0

4 cos²θ - 2√3cosθ - 2√3cosθ  + 3= 0

2cosθ (2cosθ - √3) - √3 (2cosθ - √3) = 0 

(2cosθ - √3)² = 0

cosθ = \(\frac{√3}{2}\)

{ cos30º = \(\frac{√3}{2}\) }

So, θ = 30º