Question

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

Answer 1

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