Доказать тождество (Prove identity)

1) tan^2 x - sin^2 x=sin^2 x * tan^2 x     2) (1-(sin x + cos x)^2) / (sin x * cos x - ctg x) = 2*tan^2 x       3) sin^3 x * (1 + ctg x) + cos^3 x * (1 + tan x) = sin x + cos x