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Math Help - Verify that this is an identity.

  1. #1
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    Verify that this is an identity.

    1. (tan u - cot u) / (tan u + cot u) is an identity.



    (tan u - cot u) / (tan u + cot u)
    = [(sin u/cos u) - (cos u/sin u)] / [(sin u/cos u) + (cos u/sin u)]
    = (sinē u - cosē u) / (sinē u + cosē u)
    = sinē u - cosē u



    is there any other mid steps that would be good to include?
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  2. #2
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    Re: Verify that this is an identity.

    Quote Originally Posted by JamesBond16 View Post
    1. (tan u - cot u) / (tan u + cot u) is an identity.



    (tan u - cot u) / (tan u + cot u)
    = [(sin u/cos u) - (cos u/sin u)] / [(sin u/cos u) + (cos u/sin u)]
    This is a BIG jump. You might want to break down the steps.
    = (sinē u - cosē u) / (sinē u + cosē u)
    = sinē u - cosē u



    is there any other mid steps that would be good to include?
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  3. #3
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    Re: Verify that this is an identity.

    Hello, JamesBond16!

    (tan u - cot u) / (tan u + cot u) is not an identity.
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  4. #4
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    Re: Verify that this is an identity.

    Quote Originally Posted by Soroban View Post
    Hello, JamesBond16!

    (tan u - cot u) / (tan u + cot u) is not an identity.
    Of course you're right, but it looks like JamesBond16 was proving the identity:

    (tan u - cot u) / (tan u + cot u) = sinē u - cosē u .
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