Find all values of x in the interval [0, 2π] that satisfy the equation. (Enter your answers as a comma-separated list.)? 16 cos(x) + 8 sin(2x) = 0

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Answer 1 · 2018-01-15T13:16:56

#pi/2, (3pi)/2#

#16cos(x)+8sin(2x)=0#

Divide by #8#

#2cos(x)+sin(2x)=0#

Identity:

#color(red)(sin(2x)=2sin(x)cos(x)#

#2cos(x)+2sin(x)cos(x)=0#

Factor:

#2cos(x)(1+sin(x))=0#

#2cos(x)=0#

#cos(x)=0=>x=pi/2 , (3pi)/2#

#(1+sin(x))=0#

#sin(x)=-1=>x= (3pi)/2#