Question

2sin^2(x)-8sin(x)cos(x)+7cos^2(x)=1

Answer 1

$2sin^{2}(x)-8sin(x)cos(x)+7cos^{2}(x)=1$
$2sin^{2}(x)-8sin(x)cos(x)+7cos^{2}(x)=sin^{2}(x)+cos^{2}(x)$
$sin^{2}(x)-8sin(x)cos(x)+6cos^{2}(x)=0$  $| : cos^{2}(x)$
$tg^{2}(x)-8tg(x)+6=0$

D/4=10
$tg(x)=4+ sqrt{10}$
$tg(x)=4- sqrt{10}$

$x=arctg(4+sqrt{10})+ pi *n$
$x=arctg(4- sqrt{10})+ pi *n$

n∈Z