Question

Найдите х. Нужна помощь!!!!!!

Answer 1

$1)Sin3x*Cos3x=-\frac{1}{2}|*2\\\\2Sin3xCos3x=-1\\\\Sin6x=-1\\\\6x=-\frac{\pi }{2}+2\pi n,n\in Z\\\\x=-\frac{\pi }{12}+\frac{\pi n }{3},n\in Z\\\\\\2)\frac{2tg2x}{1-tg^{2}2x}=\sqrt{3}\\\\tg4x=\sqrt{3}\\\\4x=arctg\sqrt{3}+\pi n,n\in Z\\\\4x=\frac{\pi }{3} +\pi n,n\in Z\\\\x=\frac{\pi }{12}+\frac{\pi n }{4},n\in Z$

$3)Sin^{2}2x-Cos^{2}2x=\frac{\sqrt{3}}{2} \\\\-Cos4x=\frac{\sqrt{3}}{2}\\\\Cos4x=-\frac{\sqrt{3}}{2}\\\\4x=\pm arcCos(-\frac{\sqrt{3}}{2})+2\pi n,n\in Z\\\\4x=\pm \frac{5\pi }{6}+2\pi n,n\in Z\\\\x=\pm \frac{5\pi }{24}+\frac{\pi n }{2},n\in Z\\\\\\4)2Sin^{2}4x-1=\frac{\sqrt{2}}{2}\\\\-Cos8x=\frac{\sqrt{2} }{2}\\\\Cos8x=-\frac{\sqrt{2} }{2}\\\\8x=\pm arcCos(-\frac{\sqrt{2}}{2})+2\pi n,n\in Z\\\\8x=\pm \frac{3\pi }{4}+2\pi n,n\in Z$

$x=\pm \frac{3\pi }{32}+\frac{\pi n }{4}.n\in Z$