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Math Help - Proving identities

  1. #1
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    Proving identities

    Prove that

    cos theta / 2 = sqrt[1 + (cos theta / 2)]

    I know this is somewhat similar to cosine - half of an angle identity or formula

    But I'm having trouble with the division bar, it only divides cos theta not the whole 1 + cos theta. As a result, I can't prove it

    Is (1 + cos theta ) / 2 the same to 1 + cos theta /2 ?

    Please explain, thanks
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  2. #2
    MHF Contributor kalagota's Avatar
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    Quote Originally Posted by ImKo View Post
    Prove that

    cos theta / 2 = sqrt[1 + (cos theta / 2)]

    I know this is somewhat similar to cosine - half of an angle identity or formula

    But I'm having trouble with the division bar, it only divides cos theta not the whole 1 + cos theta. As a result, I can't prove it

    Quote Originally Posted by ImKo View Post
    Is (1 + cos theta ) / 2 the same to 1 + cos theta /2 ?

    Please explain, thanks
    well, kabayan, it depends on the grouping. it will be helpful if group it properly..

    but i think, this is what you wanted to prove..

    \cos \left(\dfrac{\theta}{2}\right) = \sqrt{\dfrac{1+\cos\theta}{2}}

    if this is the case, use the indentity \cos 2\alpha = 2\cos^2 (\alpha) - 1 and let \alpha=\dfrac{\theta}{2}
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  3. #3
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    Thanks Kabayan..

    I think the book had just an error since the hint it gave is also the same as the one you gave me.
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