Question #5fa0b

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Answer 1 · 2017-03-22T17:01:52

$x=pi$

Solving for $x$ , we have:

$2cos(4x)=sqrt2$

$cos(4x)=sqrt2/2$

$4x=cos^(-1)(sqrt2/2)$

$color(red)(cos^(-1)(sqrt2/2)=pi/4)$
$color(red)("(Refer to unit circle)")$
Wikipedia

$4x = pi/4$

$x=pi$

Answer 2 · 2017-03-22T17:04:45

$x = 11.25^@, 78.75^@$

$2 cos 4 x = sqrt 2$
$cos 4 x = sqrt 2/2$

$cos 4 x = 1/sqrt 2$

$4x =cos^(-1) (1/sqrt 2)$

$4x = 45^@, 315^@$

$x =45^@/4 = 11.25^@, 315^@/4=78.75^@$ with considering $x$ are acute angles.