Question

sin в квадрате x+sinx*cosx=0

Answer 1

$\sin^2x+\sin x\cos x=0\\\sin x(\sin x+\cos x)=0\\1)\;\sin x=0\Rightarrow x=\pi n,\;n\in\mathbb{Z}\\2)\;\sin x+\cos x=0\Rightarrow \sin x=-\cos x\Rightarrow tgx=-1\\x=\frac{3\pi}4+\pi k,\;k\in\mathbb{Z}$