If 9 tan2θ - 3 = 0, find the value of 3sinθ + cos(θ) .

9 tan²α - 3 = 0

tan²α = \(\frac{3}{9}\) = \(\frac{1}{3}\)

tanθ = \(\frac{1}{\sqrt {3}}\)

θ = 30°

Now,

⇒ 3sinθ + cos(θ) = 3 × \(\frac{1}{2}\) + cos(30°)

= \(\frac{3}{2}\) + \(\frac{√3}{2}\) = \(\frac{3 + √3}{2}\)