Question

Solve for sin4x=sin2x?

Answer 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