If 7sin2θ + 3cos2θ = 4, then the value of secθ + cosecθ is?

Answer: Option B

$$\begin{array}{rl}& \text{7}{\sin }^2\theta +3\text{co}{\text{s}}^2\theta =4\\ & \text{7}{\sin }^2\theta +3\left(\text{1}-\text{si}{\text{n}}^2\theta \right)=4\\ & \text{7}{\sin }^2\theta +3-3{\sin }^2\theta =4\\ & 4{\sin }^2\theta =1\\ & {\sin }^2\theta =\frac{1}{4}\\ & \text{sin }\theta =\frac{1}{2}\\ & \sin \theta =\sin 30^{\circ }\\ & \theta =30^{\circ }\\ & \sec \theta +\mathrm{cosec}\theta \\ & =\sec 30^{\circ }+\mathrm{cosec}30^{\circ }\\ & =\frac{2}{\sqrt{3}}+2\end{array}$$