How do you find the general solutions for #cos2x = 4cosx - 3#?

1 Answer
Aug 22, 2015

Express #cos 2x# in terms of #cos^2 x#, then solve the resulting quadratic to find #cos x = 1#, hence #x = 2n pi# for any integer #n#.

Explanation:

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

#= 2 cos^2 x - 1#

So our equation becomes:

#2 cos^2 x - 1 = 4 cos x - 3#

Subtract the right hand side from the left to get:

#0 = 2 cos^2 x - 4 cos x + 2#

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

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

So #cos x = 1#

So #x = 2n pi# where #n# is any integer.