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Math Help - Identities

  1. #1
    Member purplec16's Avatar
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    Identities

    tan(x-\frac{\pi}{2})= - cot x

    \frac{tanx-tan\frac{\pi}{2}}{1+tanx+tan\frac{\pi}{2}}= -cotx

    \frac{1}{1+0}

    I cant solve this identity can someone help me?
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  2. #2
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    Hello, purplec16!

    You can't use that compound-angle formula
    . . because \tan\tfrac{\pi}{2} is undefined.


    \tan\left(x-\tfrac{\pi}{2}\right) \:=\: -\cot x

    \tan\left(x-\tfrac{\pi}{2}\right) \;=\;\frac{\sin(x-\frac{\pi}{2})}{\cos(x-\frac{\pi}{2})} \;=\;\frac{\sin x\cos\frac{\pi}{2} - \cos x\sin\frac{\pi}{2}}{\cos x\cos\frac{\pi}{2} + \sin x\sin\frac{\pi}{2}} . =\; \frac{\sin x\cdot 0 - \cos x\cdot 1}{\cos x\cdot 0 + \sin x\cdot 1} \;=\;-\frac{\cos x}{\sin x} \;=\;-\cot x

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  3. #3
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    You are entirely overlooking the fact that \tan\left(\frac{\pi}{2}\right) doesn't exist. You'll have to find some other way to proceed.

    \tan{\alpha} = \frac{\sin(\alpha)}{\cos(\alpha)}

    That might help.
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  4. #4
    Member purplec16's Avatar
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    Quote Originally Posted by TKHunny View Post
    You are entirely overlooking the fact that \tan\left(\frac{\pi}{2}\right) doesn't exist. You'll have to find some other way to proceed.

    \tan{\alpha} = \frac{\sin(\alpha)}{\cos(\alpha)}

    That might help.
    Are you implying that what he did was wrong?
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  5. #5
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    Quote Originally Posted by purplec16 View Post
    Are you implying that what he did was wrong?
    Are you not able to see the fact that both are giving the similar hint?
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  6. #6
    Member purplec16's Avatar
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    Quote Originally Posted by sa-ri-ga-ma View Post
    Are you not able to see the fact that both are giving the similar hint?
    I really dont understand what you are sayin
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  7. #7
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    Quote Originally Posted by purplec16 View Post
    Are you implying that what he [Soroban] did was wrong?
    TKH is NOT implying that at all!!

    Quote Originally Posted by purplec16 View Post
    I really dont understand what you are sayin
    For goddness sake, please read and try to process the help that people are taking the time to give you.

    Look at the timestamps on the replies by Soroban and TKH .... Soroban has actually given you the solution. And while he was giving it to you, TKH was typing a hint for you to think about.

    The only thing that defies understanding here is why you are confused.
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  8. #8
    Member purplec16's Avatar
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    Quote Originally Posted by mr fantastic View Post
    TKH is NOT implying that at all!!


    For goddness sake, please read and try to process the help that people are taking the time to give you.

    Look at the timestamps on the replies by Soroban and TKH .... Soroban has actually given you the solution. And while he was giving it to you, TKH was typing a hint for you to think about.

    The only thing that defies understanding here is why you are confused.
    Ok, thanks I guess..:S my mistake...
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