What is the principal solution of $4 c o s^{2} x - 8 c o s x + 3 = 0 ?$

$x = \frac{π}{6}$

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$x = \frac{π}{4}$

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$x = \frac{π}{3}$

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$x = \frac{π}{2}$

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Solution

The correct option is C
$x = \frac{π}{3}$

$4 c o s^{2} x - 8 c o s x + 3 = 0 4 c o s^{2} x - 8 c o s x + 4 = 1 (2 c o s x - 2)^{2} = 1 2 c o s x - 2 = \pm 1 2 c o s x = 3 - n o t p o s s i b l e 2 c o s x = 1 c o s x = \frac{1}{2} x = \frac{π}{3}$

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