Question

If |x| ≤ 1, then `2 tan^-1x + sin^-1 ((2x)/(1 + x^2))` is equal to ______.

विकल्प

• `4 tan^-1x`

• 0

• `pi/2`

• π

Answer 1

If |x| ≤ 1, then `2 tan^-1x + sin^-1 ((2x)/(1 + x^2))` is equal to `4 tan^-1x`.

Explanation:

Here, we have `2 tan^-1x + sin^-1 ((2x)/(1 + x^2))`

= `2tan^-1x + 2tan^-1x` ....`[because 2 tan^-1x = sin^-1  (2x)/(1 + x^2)]`

= 4 tan^–1x