If 6 tan2θ - 2 = 0, find the value of 3sinθ + cos2(1.5θ)

7 \(\frac{7}{2}\) 4 2

2

6 tan2θ - 2 = 0 tan2θ = \(\frac{2}{6}\) = \(\frac{1}{3}\) tanθ = \(\frac{1}{\sqrt {3}}\) θ = 30° Now, ⇒ 3sinθ + cos2(1.5θ) = 3 × \(\frac{1}{2}\) + cos2(45°) = \(\frac{3}{2}\) + \(\frac{1}{2}\)  = 2