4 sin 4x = 8 sin 2x
x=?
2 Answers

4 sin 4x = 8 sin 2x
4*2sin 2x cos 2x =  8sin 2x
or sin 2x ( cos 2x + 1) = 0
so sin 2x =0 or cos 2x = 1
or 2x = npi and 2x = npi
so x = n*pi/2 for n = 0, 1, 2,,3

8sin(2x)cos(2x) = 8sin(2x)
sin(2x)(cos(2x) + 1) = 0
sin(2x) = 0 ==> 2x = 0, pi, 2pi, 3pi
cos(2x) = 1 ==> 2x = pi, 3pi
x = 0, pi/2, pi, 3pi/2