$\left(\frac{\tan A+\sec A-1}{\tan A-\sec A+1}\right)$ is equal to

Step 1 ：Given expression: \(\frac{\tan A + \sec A - 1}{\tan A - \sec A + 1}\)

Step 2 ：Simplified expression: \(\frac{-\sqrt{2}\cos(A + \frac{\pi}{4}) + 1}{\sqrt{2}\sin(A + \frac{\pi}{4}) - 1}\)

Step 3 ：\boxed{\frac{-\sqrt{2}\cos(A + \frac{\pi}{4}) + 1}{\sqrt{2}\sin(A + \frac{\pi}{4}) - 1}}