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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.