If sec2θ + tan2θ = 7, then the value of θ when 0° ≤ θ ≤ 90° is?

Answer: Option A

$$\begin{array}{rl}& {\sec }^2\theta +\text{ta}{\text{n}}^2\theta =7\\ & \Rightarrow 1+\text{ta}{\text{n}}^2\theta +\text{ta}{\text{n}}^2\theta =7\\ & \Rightarrow 2\text{ta}{\text{n}}^2\theta =6\\ & \Rightarrow \text{ta}{\text{n}}^2\theta =3\\ & \Rightarrow \text{tan}\theta =\sqrt{3}\\ & \Rightarrow \theta =60^{\circ }\\ & \\ & \mathbf{Alternate}:\\ & \text{Take help from option }\\ & \text{put }\theta \text{ = }60^{\circ }\\ & \text{se}{\text{c}}^{2}60^{\circ }+\text{ta}{\text{n}}^{2}60^{\circ }=7\\ & {\left(2\right)}^2\text{ + }{\left(\sqrt{3}\right)}^2=7\\ & 7=7\left(\text{matched }\right)\\ & \text{So, }\theta =60^{\circ }\end{array}$$