To Prove: cosec 2x + cot 2x = cot x

Taking LHS,

= cosec 2x + cot 2x …(i)

We know that,

Replacing x by 2x, we get

So, eq. (i) becomes

[∵ 1 + cos 2x = 2 cos²x]

[∵ sin 2x = 2 sinx cosx]

= cot x

= RHS

Hence Proved