Hello, yasaminG!
secθ+cscθsecθ−cscθ=tanθ+1tanθ−1
The left side is:
.\(\displaystyle \L\frac{\frac{1}{\cos\theta}\,-\,\frac{1}{\sin\theta}}{\frac{1}{\cos\theta}\,+\,\frac{1}{\sin\theta}}\)
Multiply top and bottom by \(\displaystyle \sin\theta:\;\;\L\frac{\frac{\sin\theta}{\cos\theta}\,-\,1}{\frac{\sin\theta}{\cos\theta}\,+\,1}\;=\;\frac{\tan\theta\,-\,1}{\tan\theta\,+\,1}\)