trig

Solve for sin4x=sin2x?

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  1. sin 4x = sin 2x
    2sin 2x cos 2x - sin 2x = 0
    sin 2x(2 cos 2x - 1) =

    sin2x = 0
    so 2x = 0, π, 2π, 3π, ..
    x = 0, π/2, π , 3π/2, 2π for 0≤x≤2π

    or cos2x = 1/2
    2x = π/3, 2π-π/3, ..., the primaries
    x = π/6, 5π/6
    now, the period of cos2x is π, so adding or subtracting multiples of π will yield more answers
    x = π/6 + π = 7π/6 --> 210°
    x = 5π/6+π = 11π/6 --> 330°
    then:
    x = π/6, 5π/6, 7π/6, 11π/6 for 0≤x≤2π

    in degrees:
    x = 0,90,180,270,360 degrees
    x = 30,150, 330,210 degrees

    checking 150°
    is sin 600 = sin300 ? yes
    checking 330°
    is sin 1320 = sin660? yes

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