To Prove: cot x – 2cot 2x = tan x

Taking LHS,

= cot x – 2cot 2x …(i)

We know that,

Replacing x by 2x, we get

So, eq. (i) becomes

[∵ sin 2x = 2 sinx cosx]

[∵ 1 + cos 2x = 2 cos²x]

[∵ cos² θ + sin² θ = 1]

= tan x

= RHS

∴ LHS = RHS

Hence Proved