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Find the exact solutions of the equation in the interval [0,2pi) enter your answers as a comma
separated list
Sin 2x + sin x =0
Solution
sin2x + sinx =0
use the trig identity : sin2x = 2sinxcosx
2sinxcosx +sinx =0
sinx( 2cosx+1) =0
sinx =0
x= 0, pi in the interval [0,2pi )
cosx = -1/2
x= pi -pi/3 , pi +pi/3 (cos is -ve in IInd and IIIrd quadrant)
x = 2pi/3, 4pi/3

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