If $3 \sec \theta+4 \cos \theta-4 \sqrt{3}=0$ where $\theta$ is an acute angle then the value of $\theta$ is:
Answer & explanation
Correct answer: option 2
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