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08-12-2017
Mathematics

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Find the exact solutions of sin (2x) - sin (x) = 0 in the interval [0, 2pi)

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khorenmovsisyap0nqnn khorenmovsisyap0nqnn

08-12-2017

Sin(2x)-sin(x)=0

2sin(x)*cos(x)-sin(x)=0

sin(x)*(2cos(x)-1) = 0

Sin(x)=0 => x [PiK]
Cos(x)=1/2 => x[Pi/3+(2PiK/3)

K=0 x=0
K=1 x=Pi
K=2 x=5Pi/3

So the answer is 0,Pi, 5Pi/3

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