Can you help me with my Trigonometry Homework

Hi can you help me with my Trigonometry homework. It has to do with verifying identities and it would help a lot if you could solve maybe the first two steps.

here is the problem...

Verify: tan x +cot x = 2 csc 2x

LHS: tan x + cot x = tan x + 1/tan x = (tan^2 x + 1)/tan x = sec^2 x/tan x = 1/cos^2 x • cos x/sin x = 1/(sin x cos x) = 2/(2 sin x cos x) = 2/sin 2x = 2 csc 2x