SOLUTION: How does one prove that {{{(tanA+secA-1)/(tanA-secA+1)=(1+sinA)/cosA}}}?

Question 1114647: How does one prove that ?
Found 2 solutions by stanbon, josgarithmetic:
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
How does one prove that (tanA+secA-1)/(tanA-secA+1)=(1+sinA)/cosA
-------
Cross-multiply to get::
cos(A)(tan(A)+sec(A)-1) = (1+sin(A))(tan(A)-sec(A)+1)
-------------
sin(A) +1 -cos(A) = tanA -secA +1 + sin^2A/cos(A) - tan(A) + sin(A)
---------
-cos(A) = -sec(A) + sin^2(A)/cos(A)
-----
-cos^2(A) = -1 + sin^2(A)
-----
sin^2(A)+cos^2(A) - 1 = 0
---
0 = 0
-----------
Cheers,
Stan H.
-----------
Answer by josgarithmetic(39617) (Show Source): You can put this solution on YOUR website!
Start with the left side.

Try multiplying by .

Just a start. I have not gone any further with this. Maybe you can and will finish.
RELATED QUESTIONS
1. Prove that (1-cosA) (1-secA) = tan A sinA 2. Prove that secA (1-sinA) (secA+tanA)... (answered by mananth)
prove that sinA*secA/tanA=1 (answered by richard1234)
(tanA+secA-1)cosA (answered by Fombitz)
1/secA-tanA =secA+tanA (answered by stanbon)
(secA+tanA)(secA-tanA)=1 (answered by Alan3354)
tanA/1+cosA + sinA/1- cosA = cotA + cosecA -... (answered by Edwin McCravy)
Prove that : 1. (cscA-1)/(cscA+1) = (1-sinA)/(1+sinA) 2. (secA/cscA)+(sinA/cosA) =... (answered by Edwin McCravy)
Prove that the equations are identities.... (answered by lwsshak3)
Which identity could be used to transform the expression on the left to the one on the... (answered by lwsshak3)