Verify the identity.
cosx+cosxcot2x=cotxcscx
cos x + cos x * cot^2 x factor out cos x
cosx ( 1 + cot^2 x ) =
cos x (csc^2 x) =
cos x ( 1/ sin^2x) =
cos x ( 1/sin x) ( 1/sin x) =
(cos x / sin x) ( csc x) =
cot x csc x