Question

2sin^2-5sinxcosx-cos^2x=-2

Answer 1

$2sin^2x-5sinxcosx-cos^2x=-2 \ 2sin^2x-5sinxcosx-cos^2x=-2(sin^2x+cos^2x)\ 2sin^2x-5sinxcosx-cos^2x=-2sin^2x-2cos^2x \ 4sin^2x-5sinxcosx+cos^2x=0 Big| :cos^2x neq 0 \ 4tg^2x-5tgx+1=0$
$tg x=1$ или $tgx= frac{1}{4}$
$x= frac{ pi }{4} + pi k$ или $x= arctg frac{ 1}{4} + pi k, k in Z$