Question

докажите тождество
6 задание

Answer 1

6) tga/ (tga + ctga) = Sina/Cosa : (Sina/Cosa + Cosa/Sina) =
= Sina/Cosa : [(Sin²a + Cos²a) / Sina*Cosa] = Sina/Cosa * Sina *Cosa = Sin²a

Answer 2

$tg (a)/(tg( a)+ctg (a))=sin^2 (a) \ tg(a)/(sin(a)/cos(a)+cos(a)/sin(a))=sin^2(a) \ tg (a)/((sin^2(a)+cos^2(a))/sin(a)cos(a))=sin^2(a) \ tg(a)sin(a)cos(a)=sin^2(a) \ sin^2(a)cos(a)/cos(a)=sin^2(a) \ sin^2(a)=sin^2(a)$