4sin2theta cos2theta +(5)/(cos2theta )=(13sin2theta )/(cos2theta )

Question

4sin2theta cos2theta +(5)/(cos2theta )=(13sin2theta )/(cos2theta )

Answer 1

4sin2θcos²2θ + 5 = 13sin2θ; 4sin2θ(1 - sin²2θ) + 5 = 13sin2θ; 4sin³2θ + 9sin2θ - 5 = 0;

(sin2θ - 0.5)(4sin²2θ + 2sin2θ + 10) = 0

sin2θ - 0.5 = 0; sin2θ = 0.5 2θ = π/6 + 2πn or 2θ = 5π/6 + 2πn

θ = π/12 + πn or θ = 5π/12 + πn

And quadratic equation 4sin²2θ + 2sin2θ + 10 = 0 no real solutions (discriminant 1 - 40 = - 39 < 0)