Question

√2sin(x-3п/2)*cos(3п/2+x)+cosx=0

Answer 1

$\sqrt2*sin(x- \frac{3 \pi }{2} )*cos(\frac{3 \pi }{2} +x)+cosx=0 \\-\sqrt2*sin(\frac{3 \pi }{2}-x )*cos(\frac{3 \pi }{2} +x)+cosx=0 \\-\sqrt2*(-cosx)*sinx+cosx=0 \\\sqrt2*cosx*sinx+cosx=0\\cosx(\sqrt2*sinx+1)=0 \\ \left \{ {{cosx=0} \atop {\sqrt2*sinx+1=0}} \right.\\ \left \{ {{cosx=0} \atop {sinx=- \frac{ \sqrt2}{2} }} \right.\\ \left \{ {{x= \frac{ \pi }{2}+ \pi n, nEZ } \atop {x=(-1)^{k+1}* \frac{ \pi}{4}+\pi k, kEZ }} \right.$