Question

Using derivative prove

sec^-1x + cosec^-1x = π/2 . . . [for |x| ≥ 1]

Answer 1

Let f(x) = sec^-1x + cosec^-1x [for |x| ≥ 1] ....(1)

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, where |x| > 1 

Let x = 2. 

Then, f(2) = k ……(2)