2/(ctg^2x+1) = sin2x

ОДЗ: ctg²x≠-1 [latex] \frac{2}{ctg^2x+1} =sin2x \\ \\ \frac{2}{ \frac{1}{sin^2x} } =sin2x \\ \\ 2sin^2x-2sinxcosx=0 |:2 \\ sin^2x-sinxcosx=0|:cos^2x \neq 0 \\ tg^2x-tgx=0 \\ tgx(tgx-1)=0 \\ tgx=0~~~~~~~~~~~~~~~~~~~tgx=1 \\ x_1= \pi k,~k\in Z~~~~~~~~x_2= \frac{ \pi }{4} + \pi k,~k\in Z[/latex]