Solve: $| cos x | = cos x - 2 sin x$

x = (2 n + 1) π + \frac{π}{4}

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x = (2 n + 1) π + \frac{π}{2}

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x = 2 n π + \frac{π}{4}

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x = 2 n π + \frac{π}{2}

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Solution

The correct option is A $x = (2 n + 1) π + \frac{π}{4}$
We have, $| cos x | = cos x - 2 sin x$
Case 1)
if $cos x \geq 0$
$cos x = cos x - 2 sin x$

$\Rightarrow sin x = 0 \Rightarrow x = n π$

$∴ x = 2 n π$
Case 2)
If $cos x < 0$
$- cos x = cos x - 2 sin x$

$\Rightarrow cos x - sin x = 1$

$\Rightarrow tan x = 1 \Rightarrow x = n π + \frac{π}{4}$

$∴ x = (2 n + 1) π + \frac{π}{4}$

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