How to solve this equation? Thanks!

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Answer 1 · 2018-04-21T16:41:20

#x=(7pi)/6 or x=(11pi)/6#

Here,

#16sinx=4cos^2x-11#

#=>16sinx=4(1-sin^2x)-11#

#=>16sinx=4-4sin^2x-11#

#=>16sinx=-4sin^2x-7#

#=>4sin^2x+16sinx+7=0#

#=>4sin^2x+14sinx+2sinx+7=0#

#=>2sinx(2sinx+7)+1(2sinx+7)=0#

#=>(2sinx+1)(2sinx+7)=0#

#=>sinx=-1/2 orsinx=-7/2!in [-1,1]#

#i.e.sinx=-1/2 < 0=>color(red)(III^(rd)Quadrant or IV^(th)Quadrant#

#:.x=pi+pi/6 or x=2pi-pi/6#

#=>x=(7pi)/6 or x=(11pi)/6#