What is the value of 2 ( 1 - ^2 ) cose c^2 ^2 ( 1 + ^2 ) - 1

Answer: Option D

$$\begin{array}{rl}& \frac{2\left(1-{\sin }^2\theta \right)\text{cose}{\text{c}}^2\theta }{{\cot }^2\theta \left(1+{\tan }^2\theta \right)}-1\\ & =\frac{2{\cos }^2\theta \text{cose}{\text{c}}^2\theta }{{\cot }^2\theta {\sec }^2\theta }-1\\ & =\frac{2{\cos }^2\theta {\sin }^2\theta }{{\sin }^2\theta {\cos }^2\theta {\sec }^2\theta }-1\\ & =2{\cos }^2\theta -1\\ & =\cos 2\theta \end{array}$$