Which of the following is equal to $$\frac{1}{{\tan \theta }} + \tan \theta ?$$

Solution(By Examveda Team)

$$\eqalign{ & \frac{1}{{\tan \theta }} + \tan \theta \cr & {\text{put }}\theta = {45^ \circ } \cr & \frac{1}{1} + 1 = 2 \cr & {\text{In option}} \cr & \Rightarrow \left( {\text{A}} \right)\frac{{{\text{cosec}}\,\theta }}{{\sec \theta }} = \frac{{{\text{cosec}}\,{{45}^ \circ }}}{{\sec {{45}^ \circ }}} = \frac{{\sqrt 2 }}{{\sqrt 2 }} = 1 \cr & \Rightarrow \left( {\text{B}} \right)\sec \theta \times {\text{cosec}}\,\theta \cr & = \sec {45^ \circ } \times {\text{cosec}}\,{45^ \circ } \cr & = \sqrt 2 \times \sqrt 2 = 2 \cr & \Rightarrow \left( {\text{C}} \right)\,1 \cr & \Rightarrow \left( {\text{D}} \right){\tan ^2}\theta = {\tan ^2}{45^ \circ } = 1 \cr} $$