Use \cos ^2(x)+ \cos^2 (2x)+ \cos ^2 (3x)-1 = 2\cos^2(x)\cos(2x)(2\cos(2x)-1)
2 Answers
Arnab Kundu
·2011-10-08 04:19:46
cos^2x=\frac{1+cos2x}{2}
so the eq. in equivalent to
(1+cos2x)+(1+cos4x)+(1+cos6x)=2
or, 3+cos2x+cos6x+cos4x=2
or,(2cos2x-1)+2(cos5x)(cosx)=-1
or,2cos2x+2(cos5x)(cosx)=0
or,cosx(cosx+cos5x)=0
or,cosx{(2)(cos3x)(cos2x)}=0
so, either cosx=0 or cos2x=0 or cos3x=0
Shubhodip
·2011-10-08 04:28:49