Question

Solve the following equations.
$cos(\pi +x)\sqrt{3}sinx=sin\left(3x\frac{\pi }{2}\right),xϵ(-\frac{4\pi }{3},\frac{\pi }{2}].$

Answer 1

$cos(\pi +x)\sqrt{3}sinx=sin\left(\frac{3\pi x}{2}\right),xϵ(\frac{4\pi }{3},\frac{\pi }{2}]$

$-cosx\sqrt{3}sinx=sin\left(\frac{3\pi x}{2}\right)$

$\Rightarrow \frac{-\sqrt{3}}{2}sin2x=sin\left(\frac{3\pi x}{2}\right)$

$x\simeq -22.5,-58.03$