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Math Help - Questions in the "show that" form for exams.

  1. #1
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    Questions in the "show that" form for exams.

    Hi I have a question about the way a problem is worded and the solution you're expected to give based on that. I answered a question that said to show that for all values of \theta:
    (1+sin\theta)^2 + cos^2\theta = 2(1+sin\theta)

    I went ahead and solved it in the following manner.

    1 + 2sin\theta + sin^2\theta +cos^2\theta = 2 + 2sin\theta
    sin^2\theta + cos^2\theta = 1
    1 = 1 therefore the statement is true.

    But when I check my text book it seems to just want me to rearrange the LHS so that it's the same as the RHS. Would both the text book answer and my answer be acceptable in an exam or must it be shown in the way the text book shows it?
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  2. #2
    MHF Contributor alexmahone's Avatar
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    Re: Questions in the "show that" form for exams.

    Quote Originally Posted by Jaxx View Post
    Hi I have a question about the way a problem is worded and the solution you're expected to give based on that. I answered a question that said to show that:
    (1+sin\theta)^2 + cos^2\theta = 2(1+sin\theta)

    I went ahead and solved it in the following manner.

    1 + 2sin\theta + sin^2\theta +cos^2\theta = 2 + 2sin\theta
    sin^2\theta + cos^2\theta = 1
    1 = 1 therefore the statement is true.

    But when I check my text book it seems to just want me to rearrange the LHS so that it's the same as the RHS. Would both the text book answer and my answer be acceptable in an exam or must it be shown in the way the text book shows it?
    Your proof is correct, but unfortunately most examiners are old-fashioned and will expect you to prove it in a "standard way", like rearranging the LHS so that it's the same as the RHS.
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  3. #3
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    e^(i*pi)'s Avatar
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    Re: Questions in the "show that" form for exams.

    Quote Originally Posted by Jaxx View Post
    Hi I have a question about the way a problem is worded and the solution you're expected to give based on that. I answered a question that said to show that for all values of \theta:
    (1+sin\theta)^2 + cos^2\theta = 2(1+sin\theta)

    I went ahead and solved it in the following manner.

    1 + 2sin\theta + sin^2\theta +cos^2\theta = 2 + 2sin\theta
    sin^2\theta + cos^2\theta = 1
    1 = 1 therefore the statement is true.

    But when I check my text book it seems to just want me to rearrange the LHS so that it's the same as the RHS. Would both the text book answer and my answer be acceptable in an exam or must it be shown in the way the text book shows it?
    Only the textbook's way. The question is asking to show you can write the left form as the right.
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