Evaluate the following expression in terms of trigonometric ratios. A - A A + A

Answer: Option A

$$\begin{array}{rl}& \frac{\sec A-\tan A}{\sec A+\tan A}\\ & =\frac{\sec A-\tan A}{\sec A+\tan A}\times \frac{\sec A-\tan A}{\sec A-\tan A}\\ & =\frac{{\left(\sec A-\tan A\right)}^2}{{\sec }^{2}A-{\tan }^{2}A}\\ & =\frac{{\sec }^{2}A+{\tan }^{2}A-2.\sec A.\tan A}{1}\\ & =1+{\tan }^{2}A+{\tan }^{2}A-2.\sec A.\tan A\\ & =1+2{\tan }^{2}A-2.\sec A.\tan A\end{array}$$