SOLUTION: Prove that : (sin x - cos x + 1)/(sin x + cos x -1) = 1 / (sec x - tan x) Prove that : (tan x + sec x -1)/(tan x - sec x +1) = (1+sin x)/ cos x

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Question 878293: Prove that :
(sin x - cos x + 1)/(sin x + cos x -1) = 1 / (sec x - tan x)
Prove that :
(tan x + sec x -1)/(tan x - sec x +1) = (1+sin x)/ cos x
Answer by Edwin McCravy(20059)   (Show Source): You can put this solution on YOUR website!
Prove



LEFT SIDE = 

RIGHT SIDE = 











Now we need to show that



Let's use S for sin(x) and C for cos(x)



And work with the left side and show that it equals 



Multiply top and bottom by (S-C)-1









Since  the numerator becomes just -2SC
Write the 1 in the denominator as 







Divide top and bottom by -2S

 =



--------------------------------------

Prove



LEFT SIDE = 

RIGHT SIDE = 

Work with the left side

 =

 =

 =

 =

 =




So the identity to prove is

 = 

Using S for sin(x) and C for cos(x),

 = 

Working with the left side:

 =

Multiply by  which just equals 1:

 =

 =

 =

 =

Since , the denominator is just 2CS

 =

Write the 1 in the numerator as 

 =

 =

 =

Divide top and bottom by 2S

 =



Edwin
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