Question

Упростите выражение:
1) cosa-cosb/cosa+cosb

2) sina+sinb/ sina-sinb

Answer 1

$displaystyle frac{cos alpha-cos beta }{cos alpha +cos beta } = frac{-2sin frac{alpha + beta }{2}sin frac{alpha - beta }{2} }{2cos frac{alpha + beta }{2} cos frac{alpha - beta }{2} } =-tg bigg(frac{alpha + beta }{2} bigg)tgbigg( frac{alpha - beta }{2} bigg)$


$displaystyle frac{sin alpha + sinbeta }{sinalpha -sinbeta} = frac{2sin frac{ alpha + beta }{2} cos frac{ alpha - beta }{2} }{2sin frac{ alpha - beta }{2}cos frac{ alpha + beta }{2} } =tgbigg( frac{ alpha + beta }{2}bigg)ctgbigg( frac{ alpha - beta }{2}bigg)$