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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