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Math Help - secx + tanx = 1/(secx-tanx)

  1. #1
    Member Furyan's Avatar
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    Solved :secx + tanx = 1/(secx-tanx)

    Could someone please help me prove the following identity.

    \sec x + \tan x \equiv \dfrac{1}{\sec x -\tan x}

    I got as far as this starting with the R.H.S, but don't know if it's the right approach or how to proceed from here.

    R.H.S = \dfrac{\cos x}{1 - \sin x}

    Any help would be much appreciated, thank you.

    Now solved. I multiplied the denominator and numerator by 1 + \sin x, then it was easy.
    Last edited by Furyan; January 20th 2013 at 06:15 AM. Reason: Now solved.
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  2. #2
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    Re: secx + tanx = 1/(secx-tanx)

    You are correct, now just write it as 1/[(1-sinx)/cosx] and proceed further.
    Alternatively multiply and divide the numerator and denominator by ( secx-tanx) the numerator will reduce to 1 and you will get the RHS.
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  3. #3
    Member Furyan's Avatar
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    Re: secx + tanx = 1/(secx-tanx)

    Thank you very much for your reply, sorry I did not say in my original post, but I actually started with the R.H.S. I've now edited my post accordingly thank you.
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