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Math Help - Find all solutions of the Equation

  1. #1
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    Find all solutions of the Equation

    Any help would be appreciated for these problems. Thanks in advance

    csc(squared)x-4=0

    sec x/2 = cos x/2

    2sin(squared)x-cosx=1

    3sec(squared)x+4cos(squared)x=7
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  2. #2
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    Quote Originally Posted by ChargersFan84 View Post
    2sin(squared)x-cosx=1
    You mean 2sin²x-cosx=1 ?
    In this case just change sin²x by 1-cos²x and solve the second degree equation in cosx
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  3. #3
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    Quote Originally Posted by ChargersFan84 View Post

    1)csc(squared)x-4=0

    2)sec x/2 = cos x/2

    3)2sin(squared)x-cosx=1

    4)3sec(squared)x+4cos(squared)x=7
    1) \csc^2x-4=0

    \csc^2 x=4

    \csc x=\pm 2

    For what value of x does \csc x has 2 or -2 as its value?

    2) \sec x/2=\cos x/2

    \frac 1{\cos x/2}=\cos x/2

    \cos^2 x/2=1

    Can you proceed further?

    3) 2\sin^2-\cos x=1

    2(1-\cos^2 x)-\cos x=1

    2-2\cos^2 x-\cos x=1

    2\cos^2 x+\cos x-1=0

    Solve it...

    4)Try to do this yourself as number 3 or else i will give further hints...
    Last edited by great_math; November 27th 2008 at 07:00 PM.
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  4. #4
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    Just a small mistake in 3)
    2 cos²x + cos x - 1 = 0
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  5. #5
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    Awesome. Thanks a bunch! I can take it from there.
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  6. #6
    Member great_math's Avatar
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    Quote Originally Posted by running-gag View Post
    Just a small mistake in 3)
    2 cos²x + cos x - 1 = 0
    Sorry...

    I was asleep at that time..
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