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

Solution (By Examveda Team)

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