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    Hi !

    I know this should be really easy
    but I just can't seem to get my head round it !! :confused:

    Can anyone point me in the right direction for this question:

    SIMPLIFY
    tan^2x (cot^2x + 1) / tan^2x + 1

    :erm:

    might involve use of Pythagorean identities, i'm not sure !

    thanks xxx
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    Since cot is the inverse of tan we have,

    cot^2x * tan^2x = 1
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    and 1 + tan^2x = sec^2x
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    (Original post by john1234567)
    and 1 + tan^2x = sec^2x
    This identity is not needed.
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    :happy2:

    Thank you ever so much !!

    What a lovely welcome to TSR

    :mmm:

    I've tried 1 + tan^2x = sec^2x various times but it didn't seem to cancel out nicely

    xxx
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    I think you should end up with 1 as your answer
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    yeah

    i think cot^2x * tan^2x = 1
    hit the nail on the head ...i'm just a little confused as to how notnek managed to do it ...and so quickly !!
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    (Original post by small_fry)
    yeah

    i think cot^2x * tan^2x = 1
    hit the nail on the head ...i'm just a little confused as to how notnek managed to do it ...and so quickly !!
    Are you confused about the identity:
    cot^2x * tan^2x = 1 ?

    Let tan(x)=y

    Then cot(x) is the reciprocal of tan(x) i.e. 1/y.

    cot^2x * tan^2 x = 1/y^2 * y^2 = 1

    With a bit of practice, you should be able to spot these kind of things straight away. Another one would be:

    cosec(x)*sin(x)=1 or cosec^2(x)*sin^2(x)=1
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    that makes a lot of sense, and thank you ever so much for the other examples !

    i feel a little bit more mathematically enlightened
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    (Original post by small_fry)
    that makes a lot of sense, and thank you ever so much for the other examples !

    i feel a little bit more mathematically enlightened
    You're welcome.

    Oh and welcome to TSR, home of the best maths help forum on the net where no question is left unanswered!
 
 
 
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