Question

1+3sin^2x=2sin2x помогите

Answer 1

$1+3sin^{2} x=2sin2x$
$sin^{2}x+cos^{2} x+3sin^{2} x=4sinx*cosx$
$4sin^{2} x-2sinx*cosx+cos^{2} x=0 |:cos^{2} x$
$4tg^{2} x-4tgx+1=0$
Пусть tgx=а
$a^{2} -4a+1=0$
$D=(-4)^{2} -4*4=0$
$a= frac{4}{8} = frac{1}{2}$
$tgx= frac{1}{2}$
$x=arctg frac{1}{2} + pi n$ , n из множества Z