Solve #cos^3x=cosx#?

#Cos^3x=cosx# I get got the #0, pi/2, pi# but I cant get #(3pi)/2#. If anyone can help out I would really appreciate it.

2 Answers
Feb 10, 2018

See below

Explanation:

It's a little tricky, but try setting the equation = 0

#cos^3x=cosx#

#cos^3x-cosx=0#

Now factor out #cosx#

#cosx(cos^2x-1)=0#

And now factor the difference of two squares

#cosx(cosx+1)(cosx-1)=0#

Set each factor equal to 0 and solve using your unit circle

1) #cosx=0, x={pi/2, (3pi)/2}#

2) #cosx+1=0#

#cosx=-1, x=pi#

3) #cosx-1=0#
#cosx=1, x=0#

Feb 11, 2018

See below.

Explanation:

#cos^3(x)=cos(x)#

#cos^3(x)-cos(x)=0#

#cos(x)(cos^2(x)-1)=0#

#cos(x)*(-1)(cos^2(x)-1)=0#

#cos(x)(-cos^2(x)+1)=0#

Pythagorean identity:

#cos(x)(sin^2(x))=0#

#:.#

#cos(x)=0=>pi/2,(3pi)/2#

#sin^2(x)=0=>0, pi,2pi#