Question

sin o - cos o + 1 / sin o + cos o - 1 = 1/ sec o - tan o​

Answer 1

$\frac{sin \phi - cos \phi + 1}{sin \phi + cos \phi - 1} \\ = \frac{ \frac{sin \phi - cos \phi + 1}{cos \phi} }{ \frac{sin \phi + cos \phi - 1}{cos \phi} } \\ = \frac{tan \phi + sec \phi - 1}{tan \phi - sec \phi + 1} \\ = \frac{sec \phi + tan \phi - 1}{(tan \phi - sec \phi) + ( {sec}^{2} \phi - {tan}^{2} \phi) } \\ = \frac{sec \phi + tan \phi - 1}{(sec \phi - tan \phi)( - 1 + sec \phi + tan \phi)} \\ = \frac{1}{sec \phi - tan \phi}$