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

Solution (By Examveda Team)

$$\eqalign{ & \left( {1 + \cot \theta - {\text{cosec}}\,\theta } \right)\left( {1 + \cos \theta + \sin \theta } \right)\sec \theta \cr & \Rightarrow \left( {1 + \frac{{\cos \theta }}{{\sin \theta }} - \frac{1}{{\sin \theta }}} \right)\left( {1 + \cos \theta + \sin \theta } \right)\sec \theta \cr & \Rightarrow \frac{{\left( {\sin \theta + \cos \theta - 1} \right)\left( {\sin \theta + \cos \theta + 1} \right)}}{{\sin \theta .\cos \theta }} \cr & \Rightarrow \frac{{{{\left( {\cos \theta + \sin \theta } \right)}^2} - 1}}{{\sin \theta .\cos \theta }} \cr & \Rightarrow \frac{{1 + 2\sin \theta .\cos \theta }}{{\sin \theta .\cos \theta }} \cr & \Rightarrow 2 \cr} $$