find-the-general-solution-for-2sin-3x-sin-2x-

Question Number 79969 by Rio Michael last updated on 29/Jan/20

f i n d t h e g e n e r a l s o l u t i o n f o r

2 \sin 3 x = \sin 2 x

Answered by behi83417@gmail.com last updated on 29/Jan/20

2 (3 sinx - {4 \sin}^{3} x) = 2 sinxcosx

\Rightarrow sinx (3 - {4 \sin}^{2} x - cosx) = 0

\Rightarrow {\begin{cases} sinx = 0 \Rightarrow x = k π, k \in Z \\ 3 - 4 (1 - \cos^{2} x) - cosx = 0 \end{cases}

{4 \cos}^{2} x - cosx - 1 = 0

\Rightarrow cosx = \frac{1 \pm \sqrt{1 + 16}}{8} = \frac{1 \pm \sqrt{17}}{8}

\Rightarrow {\begin{cases} cosx = \frac{1 + \sqrt{17}}{8} \Rightarrow x = 2 m π \pm \cos^{- 1} \frac{1 + \sqrt{17}}{8} [m \in Z] \\ cosx = \frac{1 - \sqrt{17}}{8} \Rightarrow x = 2 n π \pm \cos^{- 1} \frac{1 - \sqrt{17}}{8} [n \in Z] \end{cases}

Commented by Rio Michael last updated on 30/Jan/20

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