Question

Using derivative prove

tan^-1x + cot^-1x = π/2

Answer 1

Let f(x) = tan^-1x + cot^-1x

Differentiating w.r.t. x, we get

Since, f'(x) = 0, f(x) is a constant function. 

Let f(x) = k. 

For any value of x, f(x) = k 

Let x = 0. 

Then f(0) = k ….(2)

From (1), f(0) = tan^-1(0) + cot^-1(0)