The value of $${\sec ^2}\theta $$  - $$\frac{{{{\sin }^2}\theta - 2{{\sin }^4}\theta }}{{{\text{2co}}{{\text{s}}^4}\theta - {\text{co}}{{\text{s}}^2}\theta }}$$   is?

Solution (By Examveda Team)

$$\eqalign{ & {\sec ^2}\theta - \frac{{{{\sin }^2}\theta - 2{{\sin }^4}\theta }}{{{\text{2co}}{{\text{s}}^4}\theta - {\text{co}}{{\text{s}}^2}\theta }} \cr & \Rightarrow {\sec ^2}\theta - \frac{{{{\sin }^2}\theta \left( {1 - 2{{\sin }^2}\theta } \right)}}{{{\text{co}}{{\text{s}}^2}\theta \left( {{\text{2co}}{{\text{s}}^2}\theta - 1} \right)}} \cr & \left[ {{\text{co}}{{\text{s}}^2}\theta - {{\sin }^2}\theta = 2{\text{co}}{{\text{s}}^2}\theta - 1 = 1 - 2{{\sin }^2}\theta } \right] \cr & \Rightarrow {\sec ^2}\theta - {\text{ta}}{{\text{n}}^2}\theta \cr & \Rightarrow 1 \cr} $$