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Math Help - trigonometric identity proving need help

  1. #1
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    trigonometric identity proving need help

    how should i start this

    1 - cos^2 theta/ 1 + sin theta = (convert to) sin theta

    please help
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  2. #2
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    Quote Originally Posted by xahjika View Post
    how should i start this

    1 - cos^2 theta/ 1 + sin theta = (convert to) sin theta

    please help
    1-\frac{\cos^2{\theta}}{1+\sin{\theta}}

    Recall that \cos^2{\theta} = 1-\sin^2{\theta} = (1-\sin{\theta})(1+\sin{\theta})
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  3. #3
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    it says that

    prove that it is an identity

    1 - cos^2 theta/ 1 + sin theta = sin theta
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  4. #4
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    Quote Originally Posted by xahjika View Post
    it says that

    prove that it is an identity

    1 - cos^2 theta/ 1 + sin theta = sin theta
    I have figured it out, and made the edits. But please, in the future, be more clear and add parentheses.
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  5. #5
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    That identity is not true. Are you sure you're written it correctly?

    Edit: Ah right, I was reading it incorrectly also... nevermind.
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  6. #6
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    so sorry i don't know that... i'm just copying what's on the board
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  7. #7
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    Quote Originally Posted by Chop Suey View Post
    1-\frac{\cos^2{\theta}}{1+\sin{\theta}}

    Recall that \cos^2{\theta} = 1-\sin^2{\theta} = (1-\sin{\theta})(1+\sin{\theta})

    with that do i have to foil method this? --> (1 - sin theta)(1 + sin theta)/
    1 + sin theta
    or cancel the(1 + sin theta).. / 1 + sin theta here --> (1 - sin theta)(1 + sin theta)/ 1 + sin theta
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  8. #8
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    is this right?

    red means canceled out

    1 - sin^2 theta =

    (1 - sin theta) (1 + sin theta)/ (1 + sin theta)=

    1 - ( 1 - sin theta) = sin theta
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  9. #9
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    Quote Originally Posted by xahjika View Post
    is this right?

    red means canceled out

    1 - sin^2 theta =

    (1 - sin theta) (1 + sin theta)/ (1 + sin theta)=

    1 - ( 1 - sin theta) = sin theta
    Yes, you have to cancel out like you just did. There are inconsistencies in your work that you may have to fix.
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