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Question Number 159325 by mnjuly1970 last updated on 15/Nov/21

$$$$$$\text{You can't use 'macro parameter character \#' in math mode}$$$$solve\left(\mathcal{E}quation\right)$$$$$$$$sin\left(\frac{x}{2}\right)-2sin\left(\frac{x}{3}\right)=0$$$$$$$$$$

Commented by Ar Brandon last updated on 15/Nov/21

$$x=12\pi n\pm 12\arctan \left(\sqrt{\frac{5}{7}+\frac{4\sqrt{2}}{7}}\right)$$

Answered by mr W last updated on 15/Nov/21

$$\sin \left(\frac{3x}{6}\right)-2\sin \left(\frac{2x}{6}\right)=0$$$$lett=\frac{x}{6}$$$$\sin \left(3t\right)-2\sin \left(2t\right)=0$$$$\sin t(3-4{\sin }^{2}t)-4\sin t\cos t=0$$$$\sin t(4{\cos }^{2}t-4\cos t-1)=0$$$$\sin t=0\Rightarrow t=k\pi \Rightarrow x=6k\pi$$$$4{\cos }^{2}t-4\cos t-1=0$$$$\cos t=\frac{1\pm \sqrt{2}}{2}=-\frac{\sqrt{2}-1}{2}(+rejected)$$$$\Rightarrow t=(2k+1)\pi \pm {\cos }^{-1}\frac{\sqrt{2}-1}{2}$$$$\Rightarrow x=6(2k+1)\pi \pm 6{\cos }^{-1}\frac{\sqrt{2}-1}{2}$$

Commented by mnjuly1970 last updated on 16/Nov/21

$$verynicesirW$$

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