How do you solve sin4x= -2sin2x?

2 Answers
Nghi N.
Jun 5, 2015

f(x) = sin 4x + 2sin 2x = 0

= 2sin 2x.cos 2x + 2sin 2x = 2sin 2x (cos 2x - 1)
Next, solve the 2 basic trig equations: sin 2x = 0 and cos 2x = 1.
a. sin 2x = 0 --> 2x = 0 -> x = 0
sin 2x = 0 -> 2x = pi -> x = pi/2
b. cos 2x = 1 -> 2x = 0 -> x = 0
cos 2x = 1 -> 2x = 2pi -> x = pi.

Cesareo R.
May 12, 2016

x = k( pi/2) with k = {0,1,2,3,...}

Explanation:

Making y=2x and f(y)=sin(2y)+2sin(y) = 2cos(y)sin(y)+2sin(y)=2(cos(y)-1)sin(y).The solutions of f(y)=0 are the solutions of cos(y)=1 and sin(y)=0 which are: y = 2k pi and y = (2k+1)pi. but y =2x so x = k (pi/2) with k = {0,1,2,3,...}

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