The value of ^2 - ^2 - 2 ^4 2co s^4 - co s^2 is?

Answer: Option A

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