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Math Help - Proving

  1. #1
    Junior Member Dragon's Avatar
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    Proving

    1. (1-2sin^2(x))^2  + 4sin^2(x) cos^2(x) =1

    2. 2sin(x) cos^3(x)  + 2sin^3(x)cos(x) = sin(2x)

    3. (1/4)sin (4x) = sin (x) cos^3(x) - cos (x) sin^3(x)
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  2. #2
    Eater of Worlds
    galactus's Avatar
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    The first one is not bad at all. Just expand out, but first sub in cos^{2}(x)=1-sin^{2}(x)

    (1-2sin^{2}(x))^{2}+4sin^{2}(x)(1-sin^{2}(x))

    1-4sin^{2}(x)+4sin^{4}(x)+4sin^{2}(x)-4sin^{4}(x)

    Now, see it?.
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  3. #3
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    Quote Originally Posted by Dragon View Post
    1. (1-2sin^2(x))^2  + 4sin^2(x) cos^2(x) =1

    2. 2sin(x) cos^3(x)  + 2sin^3(x)cos(x) = sin(2x)

    3. (1/4)sin (4x) = sin (x) cos^3(x) - cos (x) sin^3(x)
    2. 2sin(x) cos^3(x) + 2sin^3(x)cos(x)
    =2sin(x)cos(x)cos^2(x)+2sin(x)sin^2(x)cos(x)
    now, group 2sin(x)cos(x)together,
    and sub in sin^2(x)+cos^2(x)=1and 2sin(x)cos(x)=sin(2x)
    solved!

    3. (1/4)sin (4x) = sin (x) cos^3(x) - cos (x) sin^3(x)
    the method is similar with question 2. try it yourself. come back to me if you still have problems.
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  4. #4
    Junior Member Godfather's Avatar
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    i got number 2 but not 3
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  5. #5
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    Quote Originally Posted by Godfather View Post
    i got number 2 but not 3
    since right-hand side of question 3 is more complicated, so we start our proof from right-hand side.

    RHS: sin(x)cos^3(x)-cos(x)sin^3(x)
    =sin(x)cos(x)cos^2(x)-cos(x)sin(x)sin^2(x)
    =sin(x)cos(x)(cos^2(x)-sin^2(x))
    =(1/2)sin(2x)cos(2x)
    =(1/4)sin(4x)

    so, LHS=RHS, solved!
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