The value of (1 + cotθ - cosecθ)(1 + cosθ + sinθ)secθ =?

Answer: Option B

$$\begin{array}{rl}& \left(1+\cot \theta -\text{cosec}\theta \right)\left(1+\cos \theta +\sin \theta \right)\sec \theta \\ & \Rightarrow \left(1+\frac{\cos \theta }{\sin \theta }-\frac{1}{\sin \theta }\right)\left(1+\cos \theta +\sin \theta \right)\sec \theta \\ & \Rightarrow \frac{\left(\sin \theta +\cos \theta -1\right)\left(\sin \theta +\cos \theta +1\right)}{\sin \theta .\cos \theta }\\ & \Rightarrow \frac{{\left(\cos \theta +\sin \theta \right)}^2-1}{\sin \theta .\cos \theta }\\ & \Rightarrow \frac{1+2\sin \theta .\cos \theta }{\sin \theta .\cos \theta }\\ & \Rightarrow 2\end{array}$$