SOLUTION: prove identity (2tanx)(secx)= 1/1-sinx - 1/1+sinx

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Question 813090: prove identity
(2tanx)(secx)= 1/1-sinx - 1/1+sinx
Found 3 solutions by stanbon, Edwin McCravy, lwsshak3:
Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
(2tanx)(secx)= 1/1-sinx - 1/1+sinx
------------
(2/cos^2) = 1/(1-sin) - 1/(1+sinx)
------------
2/(1-sin^2) = 1/(1-sin) - 1/(1+sin)
------------
Multiply thru by 1-sin^2 to get:
2 = (1+sin) - (1-sin)
--------
2 = 2sin(x)
sin(x) = 1
---
x = pi/2
--------------
Cheers,
Stan H.
============

Answer by Edwin McCravy(20056) About Me  (Show Source):
You can put this solution on YOUR website!
The other "solution" is NOT a solution.  Please ignore it!
He thought it was an equation to solve, so he made a bunch of errors
and got some crazy answer. Here's the way to prove the identity:


           2tan%28x%29sec%28x%29  =   1%2F%281-sin%28x%29%29%22%22-%22%221%2F%281%2Bsin%28x%29%29

                         

                         %281%2Bsin%28x%29-1%2Bsin%28x%29%29%2F%281-sin%5E2%28x%29%29

                         2sin%28x%29%2Fcos%5E2%28x%29

                         2sin%28x%29%2F%28cos%28x%29cos%28x%29%29

                         2%2Aexpr%28sin%28x%29%2Fcos%28x%29%29%2A%281%2Fcos%28x%29%29

                         2tan%28x%29sec%28x%29
Edwin

Answer by lwsshak3(11628) About Me  (Show Source):
You can put this solution on YOUR website!
prove identity
(2tanx)(secx)= 1/1-sinx - 1/1+sinx
***
2tan%28x%29sec%28x%29=1%2F%281-sin%28x%29%29-1%2F%281%2Bsin%28x%29%29
Start with right side:
1%2F%281-sin%28x%29%29-1%2F%281%2Bsin%28x%29%29
LCD:(1+sin(x))(1-sin(x))=1-sin^2(x)
%28%281%2Bsin%28x%29%29-%281-sin%28x%29%29%29%2F%281-sin%28x%29%29%281%2Bsin%28x%29%29

verified: right side=left side