Question

4sin2xcos2xcos4x<0
Помогите срочно надо

Answer 1

$\displaystyle\bf\\4Sin2xCos2xCos4x<0\\\\\underbrace{2Sin2xCos2x}_{Sin4x}\cdot2Cos4x<0\\\\2Sin4x Cos4x<0\\\\Sin8x<0\\\\\pi +2\pi n<8x<2\pi +2\pi n \ , \ n\in Z\\\\\frac{\pi }{8} +\frac{\pi n}{4}<x<\frac{\pi }{4}+\frac{\pi n}{4} \ , \ n\in Z \\\\\\Otvet:x\in\Big(\frac{\pi }{8} +\frac{\pi n}{4} \ ; \ \frac{\pi }{4}+\frac{\pi n}{4}\Big)$