cos^2 3xcos2x−cos^2 x=0


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Question Number 42174 by lucha116 last updated on 19/Aug/18

${c o s}^{2} 3 x c o s 2 x - {c o s}^{2} x = 0$
	Answered by tanmay.chaudhury50@gmail.com last updated on 19/Aug/18

	$(\frac{1 + c o s 6 x}{2}) c o s 2 x - (\frac{1 + c o s 2 x}{2}) = 0$ $c o s 2 x + c o s 2 x . c o s 6 x - 1 - c o s 2 x = 0$ $c o s 2 x . c o s 6 x = 1$ $2 c o s 2 x . c o s 6 x = 2$ $c o s 8 x + c o s 4 x = 2$ $c o s 4 x = k$ $2 k^{2} - 1 + k - 2 = 0$ $2 k^{2} + k - 3 = 0$ $2 k^{2} + 3 k - 2 k - 3 = 0$ $k (2 k + 3) - 1 (2 k + 3) = 0$ $(2 k + 3) (k - 1) = 0$ $k - 1 = 0$ $k = 1$ $c o s 4 x = 1 = c o s o$ $4 x = 2 n Π$ $x = \frac{n Π}{2}$
	Commented by lucha116 last updated on 20/Aug/18

	$t h k s$
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