If 3 tanθ = 3sinθ, then the value of (sin2θ - cos2θ) is?

Answer: Option C

$$\begin{array}{rl}& \sqrt{3}\tan \theta =3\sin \theta \\ & \mathbf{Shortcutmethod}:\\ & \Rightarrow \sqrt{3}\frac{\sin \theta }{\cos \theta }=3\sin \theta \\ & \Rightarrow \frac{\sqrt{3}}{\cos \theta }=3\\ & \Rightarrow \cos \theta =\frac{\sqrt{3}}{3}\\ & \text{then perpendicular}=\sqrt{6}\end{array}$$

$$\begin{array}{rl}& \Rightarrow \left({\sin }^2\theta -\text{co}{\text{s}}^2\theta \right)\\ & \Rightarrow {\left(\frac{P}{H}\right)}^2-{\left(\frac{B}{H}\right)}^2\\ & \Rightarrow {\left(\frac{\sqrt{6}}{3}\right)}^2-{\left(\frac{\sqrt{3}}{3}\right)}^2\\ & \Rightarrow \frac{6}{9}-\frac{3}{9}\\ & \Rightarrow \frac{1}{3}\end{array}$$