Упростите выражение 2 (sin^2*a) - 1-tga*ctga

Tg (a) = sin (a) / cos (a)

ctg (a) = 1/tg (a) = cos (a) / sin (a)

sin (2a) = 2*sin (a) * cos (a)

(sin (a) / cos (a) + cos (a) / sin (a)) * 2*sin (a) * cos (a) = (sin (a) * sin (a) / (cos (a) * sin (a)) + cos (a) * cos (a) / (sin (a) * cos (a)) * 2*sin (a) * cos (a) = 1 / (sin (a) * cos (a)) * (sin (a) ^2+cos (a) ^2) * 2*sin (a) * cos (a) = в скобка получается 1=2