$$\frac{{1 + \cos \theta - {{\sin }^2}\theta }}{{\sin \theta \left( {1 + \cos \theta } \right)}} \times \frac{{\sqrt {{{\sec }^2}\theta + {\text{cose}}{{\text{c}}^2}\theta } }}{{\tan \theta + \cot \theta }},$$       0° < θ < 90°, is equal to:

Solution(By Examveda Team)

$$\eqalign{ & \frac{{1 + \cos \theta - {{\sin }^2}\theta }}{{\sin \theta \left( {1 + \cos \theta } \right)}} \times \frac{{\sqrt {{{\sec }^2}\theta + {\text{cose}}{{\text{c}}^2}\theta } }}{{\tan \theta + \cot \theta }} \cr & \Rightarrow \frac{{{{\cos }^2}\theta - \cos \theta }}{{\sin \theta \left( {1 + \cos \theta } \right)}} \times \frac{{\sqrt {\frac{1}{{{{\cos }^2}\theta }} + \frac{1}{{{{\sin }^2}\theta }}} }}{{\frac{{\sin \theta }}{{\cos \theta }} + \frac{{\cos \theta }}{{\sin \theta }}}} \cr & \Rightarrow \frac{{\cos \theta \left( {\cos \theta + 1} \right)}}{{\sin \theta \left( {1 + \cos \theta } \right)}} \times \frac{{\sqrt {\frac{{{{\sin }^2}\theta + {{\cos }^2}\theta }}{{{{\sin }^2}\theta {{\cos }^2}\theta }}} }}{{\frac{{{{\sin }^2}\theta + {{\cos }^2}\theta }}{{\cos \theta \sin \theta }}}} \cr & \Rightarrow \frac{{\cos \theta }}{{\sin \theta }} \times \frac{{\sqrt {\frac{1}{{{{\sin }^2}\theta {{\cos }^2}\theta }}} }}{{\frac{1}{{\cos \theta \sin \theta }}}} \cr & \Rightarrow \cot \theta \times \frac{{\frac{1}{{\cos \theta \sin \theta }}}}{{\frac{1}{{\cos \theta \sin \theta }}}} \cr & \Rightarrow \cot \theta \cr} $$