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    Solve 8cotX - 3tanX = 2

    I need help with the re-arranging

    8 1/TanX - 3 tanX = 2

    do I divide by tan?
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    (Original post by Jonario)
    Solve 8cotX - 3tanX = 2

    I need help with the re-arranging

    8 1/TanX - 3 tanX = 2

    do I divide by tan?
    Try multiplying by tanx on both sides and rearrange a little, do you notice anything? Perhaps a substitution...?
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    (Original post by zcomputer5)
    Try multiplying by tanx on both sides and rearrange a little, do you notice anything? Perhaps a substitution...?
    Ahh that just made it worse, I'm confused now D:

    8(1/tan^2X) - 3tan^2X = 2Tan

    Has this got something to do with the double angle formulae?
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    (Original post by Jonario)
    Ahh that just made it worse, I'm confused now D:

    8(1/tan^2X) - 3tan^2X = 2Tan

    Has this got something to do with the double angle formulae?
    This is just an example but what is 2X(1/2)?
    Now tell me what is AX(1/A)?
    Now what is (Tanx)x(1/tanx)?
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    If you multiply by tanx, it just turns into a simple quadratic. Just call tanx, u and maybe that'll make more sense.

    Where in the world did you get 2x from?
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    (Original post by zcomputer5)
    This is just an example but what is 2X(1/2)?
    Now tell me what is AX(1/A)?
    Now what is (Tanx)x(1/tanx)?
    Is that relevant to the question? I'm totally confused now soz
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    (Original post by Jonario)
    Is that relevant to the question? I'm totally confused now soz
    Well he's basically saying that:

    \dfrac{1}{Tanx} * Tanx = 1
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    (Original post by StephenP91)
    If you multiply by tanx, it just turns into a simple quadratic. Just call tanx, u and maybe that'll make more sense.

    Where in the world did you get 2x from?
    Tan to the power of 2 X ?

    So when I multiply by Tan i'll get

    8(1/tan^2 X ) - 3 tan^2 X = 2tan?
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    (Original post by StephenP91)
    If you multiply by tanx, it just turns into a simple quadratic. Just call tanx, u and maybe that'll make more sense.

    Where in the world did you get 2x from?
    I was trying to help him rather than just giving him the answer as if you read his last post you would of realise that he made a mistake multipling both sides through by tanx. Therefore I can him some example for him i.e. 1/2 X 2 =1!
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    (Original post by StephenP91)
    Well he's basically saying that:

    \dfrac{1}{Tanx} * Tanx = 1
    Oh my apologies, I didn't visualise it like that.
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    (Original post by Jonario)
    Tan to the power of 2 X ?

    So when I multiply by Tan i'll get

    8(1/tan^2 X ) - 3 tan^2 X = 2tan?
    You get 8 -3 tan^2 X = 2tanx
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    (Original post by zcomputer5)
    You get 8 -3 tan^2 X = 2tanx
    Yep :P

    then I rearrange to get

    3Tan^2X = 6 ?

    Then I square root the 6 and find tan^-1 ?
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    (Original post by zcomputer5)
    This is just an example but what is 2X(1/2)?
    Now tell me what is AX(1/A)?
    Now what is (Tanx)x(1/tanx)?
    you're making him confused!
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    (Original post by Jonario)
    Yep :P

    then I rearrange to get

    3Tan^2X = 6 ?

    Then I square root the 6 and find tan^-1 ?
    You've gone wrong. You end up with a quadratic equation. Let me show you.

    \dfrac{8}{Tanx} - 3Tanx = 2

    Multiply by Tanx

    8 - 3Tan^{2}x = 2Tanx

    Simply re-arrange.

    3Tan^{2}x + 2Tanx - 8 = 0

    Quadratic equation. You can either make a substitution to make it look like quadratics you've previously dealt with or simply factorise as it is. Makes no difference.
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    (Original post by Jonario)
    Yep :P

    then I rearrange to get

    3Tan^2X = 6 ?

    Then I square root the 6 and find tan^-1 ?
    Since when did 8-2tanx=6?

    No, to solve the quadratic its easiest to make a substitution, i.e. let Tanx=u to get
    3u^2 +2u -8=0 perhaps you can solve it from here?
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    (Original post by Jonario)
    Solve 8cotX - 3tanX = 2

    I need help with the re-arranging

    8 1/TanX - 3 tanX = 2

    do I divide by tan?

    tANX(8/TAnx - 3 tanx)= 2tan x

    8-3tan^2(x)=2tanx

    3tan^2(x)+2tanx - 8 = 0

    and you solve the rest
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    (Original post by TobeTheHero)
    you're making him confused!
    Well I thought that All A-level mathematians should be able to compute those fractions, I am pretty sure I learnt them for key stage 3 at school?
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    (3tanx-4)(tanx+2)=0

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    (Original post by zcomputer5)
    Since when did 8-2tanx=6?

    No, to solve the quadratic its easiest to make a substitution, i.e. let Tanx=u to get
    3u^2 +2u -8=0 perhaps you can solve it from here?
    I got (3t-4)(t+2)

    so tanX = 4/3, tan X= -2

    correct?

    Thanks guys
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    (Original post by Jonario)
    I got (3t-4)(t+2)

    so tanX = 4/3, tan X= -2

    correct?

    Thanks guys
    well done! you could always do it without using substitution
 
 
 
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