Question

1) 1+7cos^2(x)=3sin(2x) 2) sin(4x)+sin^2(2x)=0 3) 1-4sin(x)cos(x)+4cos^2(x)=0

Answer 1

$1+7(1-sin^2x)-3sin2x=0$
$1+7-7sin^2x-6sinxcosx=0$
$7sin^2x+6sinxcosx-8cos^2x-8sin^2x=0$
$- sin^2x+6sinxcosx-8cos^2x=0$
$sin^2x-6sinxcosx+8cos^2x=0$
разделим на $cos^2x \neq 0$
$tg^2x-6tgx+8=0$
D=36-32=4
tgx=4 или tgx=2
x=arctg4+$\pi k$, k∈Z или
x=arctg2+πn, n∈Z

$2sin2x*cos2x+sin^22x=0$
$sin2x(2cos2x-sin2x)=0$
$sin2x=0$ или
$(2cos2x-sin2x)=0$
2x=πn, n∈Z   
x=πn/2, n∈Z
или 
tg2x=2
2x=arctg2+πk, k∈Z
x=1/2arctg2+πk/2, k∈Z