Question

Differentiate the following w.r.t x: tan^-1(cot x) + cot^-1(tan x)

Answer 1

To find: Value of tan^-1(cot x) + cot^-1(tan x)

The formula used: (i) tan θ = cot (π/2 - θ)

(ii) cot θ = tan(π/2 - θ)

We have, tan^-1(cot x) + cot^-1(tan x)

Now, we can see that tan^-1(cot x) + cot^-1(tan x) = π - 2x

Now differentiating,