The function f (x) = tanx – x

Given f (x) = tanx – x

Applying the first derivative we get

Applying the sum rule of differentiation, so we get

Applying the derivative,

⇒ f' (x)=sec²x-1

As square of any number is always positive,

So f’(x)>0 ∀ x∈R

Hence tan x –x is always increases.

So the correct option is option A.