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