The numerical value of $$\left( {\frac{1}{{\cos \theta }} + \frac{1}{{\cot \theta }}} \right)$$   $$\left( {\frac{1}{{\cos \theta }} - \frac{1}{{\cot \theta }}} \right)$$   is?

Solution (By Examveda Team)

$$\eqalign{ & \left( {\frac{1}{{\cos \theta }} + \frac{1}{{\cot \theta }}} \right){\text{ }}\left( {\frac{1}{{\cos \theta }} - \frac{1}{{\cot \theta }}} \right) \cr & = \left( {\sec \theta + \tan \theta } \right)\left( {\sec \theta - \tan \theta } \right) \cr & = {\sec ^2}\theta - {\tan ^2}\theta \left[ {1 + {{\tan }^2}\theta = {{\sec }^2}\theta } \right] \cr & = 1 \cr} $$