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Thread: identities reveiw for grade 12 math

  1. #1
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    identities reveiw for grade 12 math

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    1)prove:tan(T)-cot(T)/tan(T)+cot(T)=2sin^2(T) - 1
    2)prove:1-cos(T)/sin(T)=sin(T)/1+cos(T)
    3)prove:1-tan^2(T)/1+tan^2(T)=1 - 2sin^2(T)

  2. #2
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    Though I don't know much about math sybols in English, it's my answer to the exercise:
    1,
    tan(T)-cot(T)/ [tan(T)+cot(T)]
    = sin^2(T)-cos^2(T)/ [sin^2(T)+cos^2(T)]
    = sin^2(T)- cos^2(T) = 2sin^2(T) - 1

    2,
    1-cos(T)/sin(T)
    = 1 - cos^2(T)/ [sin (T). (1+cos(T)]
    = sin^2(T)/ [sin (T). (1+cos(T)]
    = sin(T)/[1+cos(T)]

    3,
    1-tan^2(T)/1+tan^2(T)
    = cos^2(T) - sin^2 (T)
    = 1 - 2sin^2(T)

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