Prove identity: (sinx + cosx)^2 cscx = 2cosx + 1/sinx

Question

How do you verify the identity?

Answer 1

(sin x + cos x)^2 csc x =

(sin²x + cos²x + 2 sinx cosx)csc x =

(1 + 2 sin x cos x) csc x =

csc x + 2 sin x cos x csc x =

1/sin x + 2 sin x cos x (1/sin x) =

1/sin x + 2 cos x =

2 cos x + 1/sin x