Which of the following is equal to 1 + ?

Answer: Option B

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