Question

sin^2 2x+ cos2x*Sin2x-2cos ^2x=0
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Answer 1

$Sin^{2} 2x+Cos2x Sin2x-2Cos^{2}2x=0|:Cos^{2}2x;Cos2x\neq0 \\\\tg^{2}2x+tg2x-2=0\\\\\left[\begin{array}{ccc}tg2x=-2\\tg2x=1\end{array}\right\\\\1)tg2x=-2\\\\2x=-arctg2+\pi n,n\in Z\\\\x=-\frac{1}{2}arctg2+\frac{\pi n }{2},n\in Z\\\\2)tg2x=1\\\\2x=arctg1+\pi n,n\in Z\\\\2x=\frac{\pi }{4}+\pi n,n\in Z\\\\x=\frac{\pi }{8}+\frac{\pi n}{2} ,n\in Z$