Question

докажите тождество
tga+ctgb/ctga+tgb=tga*ctgb

Answer 1

tga+ctgb=(sinasinb+cosacosb)/cosasinb=cos(a-b)/cosasinb
tga+ctgb=(cosacosb+sinbsina)/sinacosb=cos(a-b)/sinacosb

tga+ctgb/tga+ctgb=cos(a-b)/cosasinb : cos(a-b)/sinacosb=
=cos(a-b)/cosasinb *sinacosb/cos(a-b)=tgactgb