Докажите тождество

tga+ctgb/ctga+tgb=tga*ctgb

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