(sinx+sin3x+sin5x)/(cosx+cos3x+cos5x) + 2tgx=0

(sinx+sin3x+sin5x)/(cosx+cos3x+cos5x) + 2tgx=0
(2sin3xcos2c+sin3x)/(2cos3xcos2x+cos3x)+2tgx=0
sin3x(2cos2x+1)/cos3x(2cos2x+1)+2tgx=0
tg3x+2tgx=0
(3tgx-tg³x)/(1-3tg²x)+2tgx=0
1-3tg²x≠0⇒tgx≠+-1/√3⇒x≠+-π/6+πk,k∈z
(3tgx-tg³x)+2tgx(1-3tg²x)=0
3tgx-tg³x+2tgx-6tg³x=0
5-7tg²x=0
7tg²x=5
tg²x=5/7
tgx=-√35/7⇒x=-arctg√35/7+πk,k∈z
tgx=√35/7⇒x=arctg√35/7+πk,k∈z
ответ x={πk;-arctg√35/7+πk;arctg√35/7+πk,k∈z}