Simplify the following expression cosec4A(1 - cos4 A) - 2cot2A - 1

Answer: Option D

$$\begin{array}{rl}& \text{cose}{\text{c}}^{4}A\left(1-{\cos }^{4}A\right)-2{\cot }^{2}A-1\\ & \text{Here we take }A=45^{\circ }\\ & =\text{cose}{\text{c}}^{4}45^{\circ }\left(1-{\cos }^4{45}^{\circ }\right)-2{\cot }^{2}45^{\circ }-1\\ & ={\left(\sqrt{2}\right)}^4\left\{1-{\left(\frac{1}{\sqrt{2}}\right)}^4\right\}-2\left(1\right)-1\\ & =4\left(1-\frac{1}{4}\right)-2-1\\ & =4\left(\frac{3}{4}\right)-2-1\\ & =3-2-1\\ & =0\end{array}$$