Question

Докажите тождество: (1-2cos^2(2a)/(1/2sin(4a))=tg(2a)-ctg(2a)

Answer 1

$frac{1-2cos^22 alpha }{frac{1}{2}sin4 alpha } = frac{sin^22 alpha +cos^22 alpha -2cos^22 alpha }{frac{1}{2}cdot 2sin2 alpha cdot cos2 alpha } = frac{sin^22 alpha -cos^22 alpha }{sin2 alpha cdot cos2 alpha } =\\= frac{sin^22 alpha }{sin2 alpha cdot cos2 alpha } - frac{cos^22 alpha }{sin2 alpha cdot cos2 alpha } =frac{sin2 alpha }{cos2 alpha }- frac{cos2 alpha }{sin2 alpha } =tg2 alpha -ctg2 alpha$