So unfortunate..proofs. please help!

1 + cot^2 x = csc^2 x
(cos^2 x/sin^2 x)/(1/sin^2 x) = (cos^2 x/sin^2 x) * (sin^2x / 1)
The sin^2 x terms cancel leaving only cos^2 x.
(cos^2 x/sin^2 x)/(1/sin^2 x) = (cos^2 x/sin^2 x) * (sin^2x / 1)
The sin^2 x terms cancel leaving only cos^2 x.