Solve the equation sin x + sin 2x = 0 , for 0°< x < 360°?

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Answer 1 · 2018-05-10T23:47:09

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$sin x + sin 2 x = 0$ $sinx+sin2x=0$

$sin x + [2 \cdot sin x \cdot cos x] = 0$ $sinx+[2*sinx*cosx]=0$

$sin x [1 + 2 cos x] = 0$ $sinx[1+2cosx]=0$

$sin x = 0$ $sinx=0$

$x = 0, x = 2 π or x = π$ $x=0,x=2pi or x=pi$

$1 + 2 cos x = 0$ $1+2cosx=0$

$2 cos x = - 1$ $2cosx=-1$

$cos x = - \frac{1}{2}$ $cosx=-1/2$

$x = \frac{2 π}{3} or x = \frac{4 π}{3}$ $x=(2pi)/3 or x=(4pi)/3$

note that

$sin 2 x = 2 \cdot sin x \cdot cos x$ $sin2x=2*sinx*cosx$