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

Question: If θ be an acute angle and 7sin2θ + 3cos2θ = 4, then the value of tanθ is?solution:7sin2θ + 3cos2θ = 4⇒7sin2θ + 3(1 - sin2θ) = 4 [cos2θ = 1 - sin2θ]⇒7sin2θ + 3 - 3sin2θ = 4⇒ 4sin2θ = 1⇒ sin2θ = 1/4⇒ sinθ = 1/2⇒ sinθ = sin30°∴ θ = 30°Now,tanθ= tan30∘ = 1/√3