SOLUTION: Prove that the ff equation is an identity: ((1 - tanX)/(secX)) + ((secX)/(tanX)) = ((1+tanX)/(secX)(tanX)) I end up with the left side having tan + sec^2 X as the numerato

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Question 602454: Prove that the ff equation is an identity:
((1 - tanX)/(secX)) + ((secX)/(tanX)) = ((1+tanX)/(secX)(tanX))
I end up with the left side having tan + sec^2 X as the numerator. How should I solve this properly? Please show the steps as well so that I can understand it better. Thank you.
Answer by jim_thompson5910(35256) (Show Source):
You can put this solution on YOUR website!
(1 - tanX)/(secX) + (secX)/(tanX) = (1+tanX)/(secX tanX)

(tanX(1 - tanX))/(secX tanX) + (secX)/(tanX) = (1+tanX)/(secX tanX)

(tanX - tan^2 X))/(secX tanX) + (secX)/(tanX) = (1+tanX)/(secX tanX)

(tanX - tan^2 X))/(secX tanX) + (secX*secX)/(secX tanX) = (1+tanX)/(secX tanX)

(tanX - tan^2 X))/(secX tanX) + (sec^2 X)/(secX tanX) = (1+tanX)/(secX tanX)

(tanX - tan^2 X + sec^2 X)/(secX tanX) = (1+tanX)/(secX tanX)

(tanX + sec^2 X - tan^2 X)/(secX tanX) = (1+tanX)/(secX tanX)

(tanX + 1)/(secX tanX) = (1+tanX)/(secX tanX)

(1 + tanX)/(secX tanX) = (1+tanX)/(secX tanX)

So we've shown that the original equation is indeed a true identity.