Докажите тождество: sin^2t(1+ctg^2t)-cos^2t=sin^2t

sin^2t(1+ctg^2t)-cos^2t=sin^2 t+sin^2 t*cos^2 t/sin^2 t-cos^2 t=sin^2 t+cos^2 t-cos^2 t=sin^2 t
       sin^2 t=sin^2 t