Question

2sinxcosx-2(1-2sin^2x)=1

Answer 1

$2sin xcos x-2(1-2sin^2x)=1 \ 2sin xcos x-2+4sin^2x=1 \ 2sin xcos x-3+4sin^2x=0 \ 2sin xcos x-3sin^2x-3cos^2x+4sin^2x=0 \ 2sin xcos x-3cos^2x+sin^2x=0|:cos^2x \ tg^2x+2tgx-3=0$
Пусть tg x=t(t ∈ R), тогда имеем
$t^2+2t-3=0 \ D=b^2-4ac=4+12=16 \ t_1=1 \ t_2=-3$
Возвращаемся к замене
$left[begin{array}{ccc}tg x=1 \ tgx=-3end{array}rightto left[begin{array}{ccc}x_1= frac{ pi }{4}+ pi n,n in Z\x_2=-arctg3+ pi n,n in Z end{array}right$