Question

ДОКАЖИТЕ ТОЖДЕСТВО:
$frac{1+cos2a}{1-cos2a} =ctg ^{2} a$

Answer 1

$frac{1+cos2 alpha }{1-cos2 alpha }=frac{cos^2 alpha +sin^2 alpha +(cos^2 alpha -sin^2 alpha )}{cos^2 alpha +sin^2 alpha -(cos^2 alpha -sin^2 alpha )}=frac{cos^2 alpha +sin^2 alpha +cos^2 alpha -sin^2 alpha }{cos^2 alpha +sin^2 alpha -cos^2 alpha +sin^2 alpha }=\\=frac{2cos^2 alpha }{2sin^2 alpha }=(frac{cos alpha }{sin alpha })^2=ctg^2 alpha .$