Question

1) sin 2x + cos 2x= 0
2) sin 4x - cos 2x = 0

Answer 1

$sin2x+cos 2x=0|:cos 2x \ tg2x+1=0 \ tg2x=-1 \ 2x=- frac{ pi }{4} + pi n, n in Z \ x=- frac{ pi }{8} + frac{ pi n}{2} , n in Z$

$sin 4x-cos 2x=0 \ 2sin 2xcos 2x-cos 2x=0 \ cos 2x(2sin2x-1)=0 \ left[begin{array}{ccc}cos 2x=0\sin 2x= frac{1}{2} end{array}rightto left[begin{array}{ccc}2x= frac{ pi }{2}+ pi n, n in Z\2x=(-1)^kcdot frac{ pi }{3}+ pi k, k in Z end{array}right \ \ left[begin{array}{ccc}x_1= frac{ pi }{4} + frac{ pi n}{2} , n in Z\x_2=(-1)^kcdot frac{ pi }{6} + frac{ pi k}{2},k in Zend{array}right$