Solve the trig eq

Solve the equation :
cos²x + cos²2x + cos²3x = 1 for all x

2 Answers

$c o s 2 x$ = $ 2 1 + c o s 2 x $
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

Use $cos 2 (x) + cos 2 (2 x) + cos 2 (3 x) - 1 = 2 cos 2 (x) cos (2 x) (2 cos (2 x) - 1)$

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