The value of (1 + cotθ - cosecθ)(1 + tanθ + secθ) is equal to?

Answer: Option B

$$\begin{array}{rl}& \mathbf{Shortcut}\mathbf{method}:\\ & =\left(1+\cot \theta -\mathrm{cosec}\theta \right)\left(1+\tan \theta +\sec \theta \right)\\ & \left[put,\theta ={45}^{\circ }\right]\end{array}$$
  $$=\left(1+\cot {45}^{\circ }-\mathrm{cosec}{45}^{\circ }\right)$$     $$\left(1+\tan {45}^{\circ }+\sec {45}^{\circ }\right)$$
$$\begin{array}{rl}& =\left(1+1-\sqrt{2}\right)\left(1+1+\sqrt{2}\right)\\ & =\left(2-\sqrt{2}\right)\left(2+\sqrt{2}\right)\\ & =\left[2^2-{\left(\sqrt{2}\right)}^2\right]\left[\left(a-b\right)\left(a+b\right)=a^2-b^2\right]\\ & =4-2\\ & =2\end{array}$$