Question #2c235

1 Answer
Somebody N.
Dec 30, 2017

#pi#

Explanation:

Let #u=x/2#

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

Identity: #color(red)(sin(2u)=2sin(u)cos(u))#

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

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

#cos(u)=0#

#2sin(u)+1=0#

#sin(u)=-1/2=>u=(7pi)/6 , (11pi)/6#

But #u=x/2=>x=(7pi)/3 , (11pi)/3#

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

#u=x/2=> x= pi , 3pi#

For interval #0<= x < 2pi#

#pi#

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