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Math Help - Can this Trig Identity be proven?

  1. #1
    Junior Member casey_k's Avatar
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    Post Can this Trig Identity be proven?

    I couldn't solve this one:

    1 + tan x/ 1 + cot x = 1 - tan x/ cot x - 1
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  2. #2
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    Quote Originally Posted by casey_k View Post
    I couldn't solve this one:

    1 + tan x/ 1 + cot x = 1 - tan x/ cot x - 1
    Is that \frac{1+\tan{x}}{1+\cot{x}} = \frac{1 - \tan{x}}{\cot{x} - 1}? Please put brackets where they're required...

    Turn the cots into tans. You should be able to show that both sides equal tan(x).
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  3. #3
    Junior Member casey_k's Avatar
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    Reply

    yes.
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  4. #4
    Super Member 11rdc11's Avatar
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    Yes you can prove it graphically and algebrically
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  5. #5
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    Oops, edited where I should have posted...

    Check my edit.
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  6. #6
    Junior Member casey_k's Avatar
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    ?

    how do i prove it algebraically?

    I tried to prove it and got tan but not \frac{1 - \tan{x}}{\cot{x} - 1} when i used the left side.

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  7. #7
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    Quote Originally Posted by casey_k View Post
    how do i prove it algebraically?

    I tried to prove it and got tan but not \frac{1 - \tan{x}}{\cot{x} - 1} when i used the left side.

    You've gotten the left hand side to equal tan.

    If you can show that the right hand side also equals tan, then obviously they're equal.
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