The value of ^2 cose c^2 + cose c^2 ^2 - ( ^2 + cose c^2 ) is:

Answer: Option C

$$\begin{array}{rl}& \frac{{\sec }^2\theta }{\text{cose}{\text{c}}^2\theta }+\frac{\text{cose}{\text{c}}^2\theta }{{\sec }^2\theta }-\left({\sec }^2\theta +\text{cose}{\text{c}}^2\theta \right)\\ & =\frac{{\sec }^4\theta +{\cos }^4\theta }{{\sin }^2\theta .{\cos }^2\theta }-\left(\frac{{\sin }^2\theta +{\cos }^2\theta }{{\sin }^2\theta .{\cos }^2\theta }\right)\\ & =\frac{\left({\sin }^4\theta -{\sin }^2\theta \right)+\left({\cos }^4\theta -{\cos }^2\theta \right)}{{\sin }^2\theta .{\cos }^2\theta }\\ & =\frac{-{\sin }^2\theta .{\cos }^2\theta -{\sin }^2\theta .{\cos }^2\theta }{{\sin }^2\theta .{\cos }^2\theta }\\ & =-2\\ & \mathbf{Alternate}:\\ & \text{Put }\theta =45^{\circ }\\ & 1+1-\left(2+2\right)=-2\end{array}$$