2sin(p\4+x)sin(p\4-x)+sin^2x=0

Используем формулу: [latex]sin^2a - sin^2b = sin(a+b)sin(a-b)\\ \\2sin(\frac{\pi}{4}+x)sin(\frac{\pi}{4}-x)+sin^2x=0\\2sin^2\frac{\pi}{4}-2sin^2x+sin^2x=0\\2*(\frac{\sqrt2}{2})^2-sin^2x=0\\1-sin^2x=0\\sinx=\pm1\\\\1)sinx=1\\x=\frac{\pi}{2}+2\pi n, \; n\in Z;\\\\2)sinx=-1\\x=-\frac{\pi}{2}+2\pi k, \; k\in Z.\\[/latex]