cos(y) sin(y)= cs c(y)

The identity as you entered it is incorrect:


\cos(y) \sin(y) \ne \csc(y)


In general for these types of problems it's best to convert funtions of tan, cot, sec, and csc to their sine and cosine equivalents. Then you can usually apply other identities to complete the proof: such as:


\sin^2x +\cos^2x =1 \\
\sin(2x) = 2 \sin(x) \cos(x) \\
\cos(2x) = \cos^2x - \sin^2x = 1 - 2 \sin^2x = 2 \cos^2 x - 1