सिद्ध कीजिए कि - `(tan A+sec A-1)/(tan A - sec A+1)=(1+sin A)/(cos A)`.

Explanation

`L.H.S.=(tan A+sec A-1)/(tan A-sec A+1)`
`= (tan A + sec A -(sec^(2)A-tan^(2)A))/(tan A-sec A+1)`
`=((tan A+sec A)-(sec A+tan A)(sec A-tan A))/(tan A - sec A+1)`
`= ((tan A+sec A)(1-sec A + tan A))/(tan A - sec A+1)`
`=((sec A+tan A)(tan A - sec A+1))/((tan A - sec A +1))=sec A + tan A`
`=(1)/(cos A)+(sin A)/(cos A)=(1+sin A)/(cos A)=R.H.S. " "` इति सिद्धम्