Question

решите неравенство
$cosxsinx$≤$\frac{1}{4}$

Answer 1

$Cosx Sinx\leq \frac{1}{4}\\\\Cosx Sinx*2\leq \frac{1}{4}*2\\\\Sin2x\leq\frac{1}{2}\\\\-\pi-arc Sin\frac{1}{2}+2\pi n \leq2x\leq arc Sin\frac{1}{2}+2\pi n,n\in Z\\\\-\pi-\frac{\pi }{6}+2\pi n\leq2x\leq\frac{\pi }{6}+2\pi n,n\in Z\\\\-\frac{7\pi }{6}+2\pi n\leq2x\leq\frac{\pi }{6}+2\pi n,n\in Z\\\\-\frac{7\pi }{12}+\pi n\leq x\leq\frac{\pi }{12}+\pi n,n\in Z\\\\Otvet:\boxed{x\in[-\frac{7\pi }{12}+\pi n;\frac{\pi }{12}+\pi n],n\in Z}$