Question

Упростите выражение:сtga+ctgB/sin(a+B)

Answer 1

$frac{ctg alpha +ctg beta }{sin( alpha + beta )}= frac{ frac{cos alpha }{sin alpha } + frac{cos beta }{sin beta } }{sin alpha cdot cos beta +sin beta cdot cos alpha } = frac{cos alpha cdot sin beta +cos beta cdot sin alpha }{sin alpha cdot cos beta cdot (sin alpha cdot cos beta +sin beta cdot cos alpha )} =\\=frac{1}{sin alpha cdot cos beta }$