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Math Help - Proving the identity

  1. #1
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    Proving the identity

    I just started A-level maths and I couldn’t able to do this maths question.
    Prove the identity
    1/(cosecx-1) - 1/(cosecx+1) = 2(tan^2)x
    Can you please help me out if you can thanks.
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  2. #2
    MHF Contributor harish21's Avatar
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     L.H.S. = \frac{1}{csc(x)-1} - \frac{1}{csc(x)+1} = \frac{csc(x)+1-(csc(x)-1)}{(csc(x)-1)(csc(x)+1}

    now simplify and complete!!

    Note:  csc^{2}(x) - cot^{2}(x) = 1
    Last edited by harish21; October 8th 2010 at 02:11 PM.
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  3. #3
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    Quote Originally Posted by harish21 View Post
     L.H.S. = \frac{1}{csc(x)-1} - \frac{1}{csc(x)+1} = \frac{csc(x)+1-(csc(x)-1)}{(csc(x)-1)(csc(x)+1}

    now simplify and complete!!

    Note:  csc^{2}(x) - cot^{2}(x) = 1
    ok this is what i have after simplifying.

    2/(cosecx-1)

    i am not sure if i am correct or not and What do i do next?
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  4. #4
    MHF Contributor harish21's Avatar
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    NOOOO....

     \frac{csc(x)+1-(csc(x)-1)}{(csc(x)-1)(csc(x)+1}= \frac{2}{csc^{2}(x)-1} = \frac{2}{cot^{2}(x)} = 2 \times \frac{1}{cot^{2}(x)} = 2tan^{2}(x)

    Remember that:

     (csc(x)-1)(csc(x)+1) = csc^{2}(x)-1 BECAUSE (a-b)(a+b) = a^2-b^2

    Hope this helps..
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