find-the-general-solution-of-the-equation-2sin-3-sin-2-

Question Number 84134 by Rio Michael last updated on 09/Mar/20

find the general solution of the equation

2 \sin 3 θ = \sin 2 θ

Answered by mr W last updated on 09/Mar/20

2 \sin θ (3 - 4 \sin^{2} θ) = 2 \sin θ \cos θ

\sin θ (4 \cos^{2} θ - \cos θ - 1) = 0

\Rightarrow \sin θ = 0

\Rightarrow θ = k π

o r

\Rightarrow 4 \cos^{2} θ - \cos θ - 1 = 0

\Rightarrow \cos θ = \frac{1 \pm \sqrt{17}}{8}

\Rightarrow θ = 2 k π \pm \cos^{- 1} \frac{1 + \sqrt{17}}{8}

\Rightarrow θ = (2 k + 1) π \pm \cos^{- 1} \frac{\sqrt{17} - 1}{8}

Commented by Rio Michael last updated on 09/Mar/20

thanks sir