Question

20 баллов!!!! Упростите выражения

Answer 1

$frac{1}{sin alpha -sin 3 alpha } - frac{1}{sin3 alpha -sin 5 alpha } = frac{1}{-2sin alphacdotsin2 alpha } + frac{1}{2sin alpha cdotsin 4 alpha } = \ \ = frac{-sin4 alpha +sin2 alpha }{2sin alpha sin2 alpha sin4 alpha } = frac{-2sin2 alpha cos2 alpha +sin2 alpha }{2sin alpha sin2 alpha sin4 alpha} = frac{-sin2 alpha (cos2 alpha -1)}{2sin alpha sin2 alpha sin4 alpha} =frac{-cos2 alpha +1}{2sin alpha sin4 alpha }=$
$= frac{-cos^2 alpha +sin^2 alpha +cos^2 alpha +sin^2 alpha }{2sin alpha sin4 alpha } = frac{2sin^2 alpha }{2sin alpha sin4 alpha} = frac{sin alpha }{sin4 alpha }$

Answer 2

Максиму упростил

Answer 3

http://znanija.com/task/10725683