Question

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

Answer 1

$2sin x cos x+2(1-sin^2x)=1 \ 2sin x cos x+2-2sin^2x=1 \ 2sin xcos x+1-2sin^2x=0 \ 2sin xcos x+sin^2x+cos^2x-2sin^2x=0 \ 2sin xcos x+cos^2x-sin^2x=0|:cos^2x \ tg^2x-2tgx-1=0$
Пусть tg x = t, тогда
t²-2t-1=0
D=b²-4ac=4+4=8
t1=1+√2
t2=1-√2
Возвращаемся к замене
$tg x=1pm sqrt{2} \ x=arctg(1pm sqrt{2} )+ pi n,n in Z$