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Solve the following equation: , 4x , + , 2 , ^2 , x , = ,1.

Question

Solve the following equation:
$cos 4 x + 2 cos^{2} x = 1.$

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Mateo Discussed

Solve the following equation:

cos 4 x + 2 cos^{2} x = 1.

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Text solutionVerified

2 cos^{2} 2 x - 1 = 1 - 2 cos^{2} x = - cos 2 x

Let

cos 2 x = z .

2 z^{2} + z - 1 = 0

(2 z - 1) (z + 1) = 0

So,

cos 2 x = - 1

and

cos 2 x = \frac{1}{2} .

∴

x = (2 n + 1) \frac{π}{2}

and

x = nπ \pm \frac{π}{6} .

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Question Text	Solve the following equation: $cos 4 x + 2 cos^{2} x = 1.$
Answer Type	Text solution:1
Upvotes	150