Question

Sin2x/sin(3p/2-x)= sqrt2

Answer 1

$\frac{Sin2x}{Sin(\frac{3\pi }{2}-x) }=\sqrt{2}\\\\\frac{2SinxCosx}{-Cosx}=\sqrt{2}\\\\-2Sinx=\sqrt{2}\\\\Sinx=-\frac{\sqrt{2} }{2} \\\\x=(-1)^{n}arcSin(-\frac{\sqrt{2} }{2})+\pi n,nez\\\\x=(-1)^{n} (-\frac{\pi }{4})+\pi n,nez\\\\x=(-1)^{n+1}\frac{\pi }{4}+\pi n,nez$