SOLUTION: Verify the identity (secx-tanx)^2= 1-sinx/1+sinx

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Question 763428: Verify the identity (secx-tanx)^2= 1-sinx/1+sinx
Answer by DrBeeee(684) About Me  (Show Source):
You can put this solution on YOUR website!
Show that
(1) (secx - tanx)^2 = (1-sinx)/(1+sinx)
Let secx = 1/cosx and tanx = sinx/cosx in (1) and get
(2) (1/cosx - sinx/cosx)^2 = (1-sinx)/(1+sinx) or
(3) ((1 - sinx)/cosx)^2 = (1-sinx)/(1+sinx) or
(4) (1 - sinx)^2/(cosx)^2 = (1-sinx)/(1+sinx) or
(5) (1 - sinx)(1 - sinx)/(cosx)^2 = (1-sinx)/(1+sinx)
Now let cosx^2 = 1 - sinx^2 in (5) and get
(6) (1 - sinx)(1 - sinx)/(1 - sinx^2) = (1-sinx)/(1+sinx)
Now note that (1 - sinx^2) = (1 - sinx)*(1 + sinx) so we have
(7) (1 - sinx)/(1 + sinx) = (1-sinx)/(1+sinx) QED