Question

( sin x - 3 cos x ) ( cos x + sin x ) = 1

Answer 1

Раскроем скобки сначала
$sin xcos x-3cos^2 x+sin^2 x-3cos xsin x=1\ \ sin^2 x-2cos xsin x-3cos^2x=sin^2 x+cos^2 x\ \ 4cos^2x+2cos xsin x=0\ \ 2cos x(2cos x+sin x)=0\ \ left[begin{array}{ccc}cos x=0\ 2cos x+sin x=0end{array}rightto left[begin{array}{ccc}cos x=0\ tg x=-2end{array}rightto left[begin{array}{ccc}x_1= frac{pi}{2}+ pi n,n in Z\ x_2=-arctg2+ pi n,n in Z end{array}right$