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March 27, 2017

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can you prove this equation for me?

sin2x X sec2x = 2sinx

  • Math - ,

    by "proving" an equation , we usually mean to show that it is an identity.
    but it is NOT an identity.
    (I usually just try it with an arbitrary angle)
    sin2x/cos2s = 2sinx
    tan 2x = 2sinx
    let x= 30°
    LS = tan 60 = √3
    RS = 2sin30 = 2(1/2) = 1
    LS ≠ RS
    So it is not an identity, (all we need is one exception)

    If you are solving for x, then
    2sinx cosx (1/cos2x) = 2sinx
    2sinxcosx(1/(2cos^2x - 1) = 2sinx
    2sinxcosx = 2sinx(2cos2x - 1)
    2sinxcosx - 2sinx(2cos^2x - 1) = 0
    2sinx [ cosx - 2cos^2x + 1] = 0
    2sinx = 0 or 2cos^2x - cosx - 1) = 0
    sinx = 0
    x = 0, 180°, 360°

    2cos^2x - cosx - 1) = 0
    (2cosx + 1)(cosx - 1) = 0
    cosx = -1/2 or cosx = 1

    cosx = -1/2
    x = 120°, 240°

    cosx = -1
    x = 270°

    x = 0, 180, 360, 120, 240, 270 °
    I gave the angles in degrees, and in the domain between 0 and 360
    I assume you know how to change them to radians if necessary.

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