What is the value of [ 1 - ( 90^ - ) ]^2 [ ^2 ( 90^ - ) ] - 1 = ?

Answer: Option A

$$\begin{array}{rl}& \frac{{\left[1-\tan \left({90}^{\circ }-\theta \right)\right]}^2}{\left[{\cos }^2\left({90}^{\circ }-\theta \right)\right]}-1\\ & \text{By putting }\theta =45^{\circ }\\ & \Rightarrow \frac{{\left[1-\tan \left({90}^{\circ }-{45}^{\circ }\right)\right]}^2}{\left[{\cos }^2\left({90}^{\circ }-{45}^{\circ }\right)\right]}-1\\ & \Rightarrow \frac{{\left[1-\tan {45}^{\circ }\right]}^2}{{\cos }^2{45}^{\circ }}-1\\ & \Rightarrow 0-1\\ & \Rightarrow -1\\ & \text{By satisfying in option A}\\ & \Rightarrow -\sin 2\theta \\ & \Rightarrow -\sin 90^{\circ }\\ & \Rightarrow -1\end{array}$$