A good approach with these proofs is to reduce everything to sine and cosine only. Then you find the steps are easier to simplify, and it is easier to recognise the various formulas we have learned.

`"LHS"=2\ csc\ 2x\ tan\ x`

`=(2 tan x)/(sin 2x)`

`=(2 tan x)/(2 sin x cos x)`

`=(sin x)/(cos x)xx1/(sin x cos x)`

`=1/(cos^2x)`

`=sec^2x`

`="RHS"`

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