Question

$sin^{2} x+sin2x=0$

Answer 1

$sin^2x+sin2x=0;\\sin^2x+2sinxcosx=0;\\sinx(sinx+2cosx)=0.$

$sinx=0;$

$x=\pi n, n$∈$Z$.

$sinx+2cosx=0;\\sinx=-2cosx|:cosx\neq0;\\tgx=-2;$

$x=-arctg2+\pi n,$∈$Z$.

Ответ: x∈{πn; -arctg2+πn | n∈Z}.