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)   (Show Source): You can put this solution on YOUR website!
(2tanx)(secx)= 1/1-sinx - 1/1+sinx
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(2/cos^2) = 1/(1-sin) - 1/(1+sinx)
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2/(1-sin^2) = 1/(1-sin) - 1/(1+sin)
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Multiply thru by 1-sin^2 to get:
2 = (1+sin) - (1-sin)
--------
2 = 2sin(x)
sin(x) = 1
---
x = pi/2
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Cheers,
Stan H.
============
Answer by Edwin McCravy(20056)   (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:


             =   

                         

                         

                         

                         

                         

                         
Edwin
Answer by lwsshak3(11628)   (Show Source): You can put this solution on YOUR website!
prove identity
(2tanx)(secx)= 1/1-sinx - 1/1+sinx
***

Start with right side:

LCD:(1+sin(x))(1-sin(x))=1-sin^2(x)


verified: right side=left side
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