6 sin 2θ tan θ = 4, where 0º < θ < 90º
sin 2θ = 2sin θ cos θ and tanθ = sinθcosθ\frac{\sin\theta}{\cos\theta}cosθsinθ
= 6 x 2sin θ cos θ x sinθcosθ=4\frac{\sin\theta}{\cos\theta} = 4cosθsinθ=4
= sin2θ=4\sin^2 \theta = 4sin2θ=4
= sin2θ=412=13\sin^2 \theta = \frac{4}{12} = \frac{1}{3}sin2θ=124=31
=sinθ=13=13\sin \theta = \frac{\sqrt{1}}{3} = \frac{1}{\sqrt[3]{}}sinθ=31=31
= θ=sin−1(13)\theta = \sin^{-1}\left(\frac{1}{\sqrt[3]{}}\right)θ=sin−1(31)
∴ θ = 35.26º
