If θ be an acute angle and 7sin2θ + 3cos2θ = 4, then the value of tanθ is?

Answer: Option B

$$\begin{array}{rl}& \text{7}{\sin }^2\theta +3{\cos }^2\theta =4\\ & \Rightarrow \text{7}{\sin }^2\theta +3\left(1-{\sin }^2\theta \right)=4\\ & \Rightarrow \text{7}{\sin }^2\theta +3-3{\sin }^2\theta =4\\ & \Rightarrow 4{\sin }^2\theta =1\\ & \Rightarrow {\sin }^2\theta =\frac{1}{4}\\ & \Rightarrow \sin \theta =\frac{1}{2}\\ & \Rightarrow \sin \theta =\sin 30^{\circ }\\ & \Rightarrow \theta =30^{\circ }\\ & \tan 30^{\circ }=\frac{1}{\sqrt{3}}\\ & \\ & \mathbf{Alternate}:\\ & \text{Put}\theta =30^{\circ }\\ & \text{7}\times {\sin }^{2}30^{\circ }+3{\cos }^{2}30^{\circ }=4\\ & \Rightarrow 7\times \frac{1}{4}+3\times \frac{3}{4}=4\\ & \Rightarrow \frac{7}{4}+\frac{9}{4}=4\\ & \Rightarrow \frac{16}{4}=4\\ & \Rightarrow 4=4\left(\text{Satisfied}\right)\\ & \therefore \tan 30^{\circ }=\frac{1}{\sqrt{3}}\end{array}$$