SOLUTION: 1/secx+1 - 1/secx-1

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Question 760385: 1/secx+1 - 1/secx-1
Found 2 solutions by Alan3354, DrBeeee:
Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
1/secx+1 - 1/secx-1
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= ((sec - 1) - (sec+1))/(sec^2 - 1)
= -2/(sec^2 - 1)
= -2/tan^2
= -2cot^2

Answer by DrBeeee(684) About Me  (Show Source):
You can put this solution on YOUR website!
Let y = 1/(secx - 1) - 1/(secx - 1) which after cross muliplying becomes
(2) y = [(secx - 1) - (secx + 1)]/[(secx + 1)*(secx - 1)] or
(3) y = [-2]/[secx^2 - 1] or using the identity
(4) tanx^2 = secx^2 - 1 we have
(5) y = -2/tanx^2 or
(6) y = -2cotx^2