Which of the following is equal to [ + - 1 - + 1 ]?

Answer: Option A

$$\begin{array}{rl}& \left[\frac{\tan \theta +\sec \theta -1}{\tan \theta -\sec \theta +1}\right]\\ & =\left[\frac{\tan \theta +\sec \theta -\left({\sec }^2\theta -{\tan }^2\theta \right)}{\left(\tan \theta -\sec \theta +1\right)}\right]\\ & =\frac{\left(\sec \theta +\tan \theta \right)\left[1-\sec \theta +\tan \theta \right]}{\left(\tan \theta -\sec \theta +1\right)}\\ & =\sec \theta +\tan \theta \\ & =\frac{1}{\cos \theta }+\frac{\sin \theta }{\cos \theta }\\ & =\frac{1+\sin \theta }{\cos \theta }\end{array}$$