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  1. #1
    Banned Ultimus's Avatar
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    This is the hardest trigonometry problem I've ever seen, reps available.

    Ok I have been studying for my trig exam for 4 hours strait, and I'm on my last problem I can't figure out.

    It says simplify:



    The back of the book says the answer is "1-sin x" but I cant get it simplified that far.
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  2. #2
    Registered User BTBAM's Avatar
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    are those 2s?
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  3. #3
    Banned Ultimus's Avatar
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    Originally Posted by BTBAM View Post
    are those 2s?
    correct, dividing the X by 2 but not the whole problem
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  4. #4
    Registered User MikeDre's Avatar
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    Prob goes to Cos^2(x) + Sin^2(X) which goes to 1 then blah blah blah

    I dunno
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  5. #5
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    expand what's inside: [cos(x/2) + sin(x/2)^2] - 2sin(x/2)cos(x/2)

    recognize that you have cos(y)^2 + sin(y)^2

    = 1 - 2sin(x/2)cos(x/2)

    recognize that you have a double angle identity on the right

    = 1-sin(x)
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  6. #6
    Banned Ultimus's Avatar
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    Originally Posted by SlammaJamma View Post
    expand what's inside: [cos(x/2) + sin(x/2)^2] - 2sin(x/2)cos(x/2)

    recognize that you have cos(y)^2 + sin(y)^2

    = 1 - 2sin(x/2)cos(x/2)

    recognize that you have a double angle identity on the right

    = 1-sin(x)
    how did you expand that in the first step?
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  7. #7
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    Originally Posted by Ultimus View Post
    how did you expand that in the first step?
    Just expand it like you would anything else. foil I guess

    I put brackets just to show that what's inside reduces to 1
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  8. #8
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    Originally Posted by Ultimus View Post
    Ok I have been studying for my trig exam for 4 hours strait, and I'm on my last problem I can't figure out.

    It says simplify:



    The back of the book says the answer is "1-sin x" but I cant get it simplified that far.
    This is basically like proving the identity...except without the right hand side given.

    Sin(x/2) = +- sq root( 1-cosx/2)
    Cos(x/2) = +- sq root (1+cosx/2)

    Since its squared the roots cancel out and all you have to do is combine after getting the lcd and you wind up with 1-sinx.
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  9. #9
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    The answer is one my son.


    well in short its 1 sin...but its really


    1.000000000000000000000000000000000000000000000000 0000000000000000000000001
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  10. #10
    Registered User FltMech's Avatar
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  11. #11
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    Originally Posted by FltMech View Post
    rofl what's that from?
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