Question

Sprawdz tozsamosc trygonometryczna
(sin α + cos α)(tg α + ctg α)=1/sin α+ 1/ cos α

Answer 1

(sinα+cosα)(tgα+ctgα)=(sinα+cosα)[(sinα/cosα)+(cosα/sinα)]
=(sin²α/cosα)+cosα+sinα+(cos²α/sinα)=
=(1/cosα)(sin²α+cos²α) +(1/sinα)(sin²α+cos²α)=1/cosα+1/sinα