sin(x+π3)+2sin(x−π3)=0\sin\left(x+\frac{\pi}{3}\right)+2\sin\left(x-\frac{\pi}{3}\right)=0sin(x+3π)+2sin(x−3π)=0 sinx⋅cosπ3+cosx⋅sinπ3+2sinx⋅cosπ3−2cosx⋅sinπ3=3sinx⋅cosπ3−cosx⋅sinπ3=32sinx−32cosx=0\sin x \cdot \cos\frac{\pi}{3} + \cos x \cdot \sin\frac{\pi}{3} + 2\sin x \cdot \cos\frac{\pi}{3} - 2\cos x \cdot \sin\frac{\pi}{3} = 3\sin x \cdot \cos\frac{\pi}{3} - \cos x \cdot \sin\frac{\pi}{3} = \frac{3}{2}\sin x - \frac{\sqrt{3}}{2}\cos x = 0sinx⋅cos3π+cosx⋅sin3π+2sinx⋅cos3π−2cosx⋅sin3π=3sinx⋅cos3π−cosx⋅sin3π=23sinx−23cosx=0 3sinx−3cosx=023sin(x−θ)=0tanθ=13θ=π6,76π3\sin x - \sqrt{3}\cos x = 0 \qquad 2\sqrt{3}\sin(x-\theta) = 0 \qquad \tan\theta = \frac{1}{\sqrt{3}} \qquad \theta = \frac{\pi}{6}, \frac{7}{6}\pi3sinx−3cosx=023sin(x−θ)=0tanθ=31θ=6π,67π これから x=π6,76πx = \dfrac{\pi}{6}, \dfrac{7}{6}\pix=6π,67π