Question

Упростите выражение .

Answer 1

$= frac{1-cos alpha }{1+cos alpha} - frac{1-2cos alpha }{1-cos^2 alpha} =frac{1-cos alpha }{1+cos alpha} -frac{1-2cos alpha }{(1-cos alpha)(1+cos alpha )} = \ = frac{(1-cos alpha )^2-(1-cos alpha )}{1-cos^2 alpha } = frac{1-2cos alpha +cos^2 alpha -1+2cos alpha }{sin^2 alpha }= frac{cos^2 alpha }{sin^2 alpha} =ctg^2 alpha .$