Question

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

Answer 1

ОДЗ: ctg²x≠-1

$frac{2}{ctg^2x+1} =sin2x \ \ frac{2}{ frac{1}{sin^2x} } =sin2x \ \ 2sin^2x-2sinxcosx=0 |:2 \ sin^2x-sinxcosx=0|:cos^2x neq 0 \ tg^2x-tgx=0 \ tgx(tgx-1)=0 \ tgx=0~~~~~~~~~~~~~~~~~~~tgx=1 \ x_1= pi k,~kin Z~~~~~~~~x_2= frac{ pi }{4} + pi k,~kin Z$