sin a (sin a/(1-cos a) - 1/tg a) =
=sin a (sin a*tga- (1-cos a))/tg a =
=cos a *(sin a*tga- 1+cos a)=
=sin^2 a - cos a+cos^2 a=1-cos a=2sin ^2 (a\2)
(использовали формулу sos a*tga=sin a)
