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    (Original post by happysunshine)
    Is this from Maths/Further Maths A-Level?
    Just Maths A Level.
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    (Original post by ShOcKzZ)
    solve, for 0<x<2pi

    2sinXcos2X + sin2X = 0

    thanks
    2sinxcos2x + sin2x = 0

    2sinXcos2X + 2sinXcosX = 0

    2(sinXcos2X + sinXCosX) = 0

    sinXcos2X + sinXcosX = 0

    so, the solution are the x values when sinXcos2X = -sinXcosX

    0, pi/3, pi, 5pi/3, 2pi

    (I have checked answers on a graphic calculator and i'm as sure as i can be that they're right)
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    i did it this way....

    sin2X = 2SinxCosx

    so.. 2sinXcos2X + 2SinxCosx = 0

    = 2Sinx ( cos2x + cos x) = 0

    since you are finding solutions for = 0, you just needed to solve each factor to 0....


    2Sinx = 0 @ 0 & 2pi

    cos 2x + cos x = 0

    written as..... cos2x = - cos x

    with solutions at x = pi/3 , pi, 5 pi/3


    therefore total soultions between 0 and 2 pi are...

    0, pi/3, pi, 5 pi/3, 2 pi ...... i think
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    (Original post by Mysticmin)
    Right, here goes...

    2sinXcos2X + sin2X = 0
    2SinX(Cos^2X - Sin^2X) + 2SinxCosX=0
    2SinX(Cos^2X - Sin^2X + CosX) = 0
    2SinX(Cos^2X - (1- Cos^2X) + CosX) = 0
    2SinX(2Cos^2X + CosX -1) = 0
    2SinX(2CosX + 1)(CosX - 1) = 0

    SinX = 0 --> X = 0, 180, 360
    CosX = 1 --> X = 0 or 360.
    CosX = -1/2 ---> X = 120, 240.

    answers: 0, 120, 180, 240, 360.
    or in radians: 0, 2pi/3, pi, 4pi/3, 2pi.

    did that work out right? Someone check my algebra...i make silly mistakes often.
    yeah thats exactly right, except for its 5pi/3 not 4pi/3, all your working is correct so it's probably just a typo.
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    (Original post by iiikewldude)
    yeah thats exactly right, except for its 5pi/3 not 4pi/3, all your working is correct so it's probably just a typo.
    wouldn't 5pi/3 made 300 degrees? and cosine 300 is positive.
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    (Original post by Turnip09)
    Ralfskini is wrong.

    dont be startled its an easy error-

    it works out at 2cosx= 1/2

    and therefore sin^2-cos= 1/2

    factorise from here and bob's your uncles brother.


    I think you should check your maths. Im pretty sure mine is right.
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    someone strong at mechanics, could you visit the academic forum please?

    ta !
 
 
 
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