Question

`sin(tan^-1x), |x| < 1` is equal to

Options

• `x/sqrt(1 - x^2)`

• `1/sqrt(1 - x^2)`

• `1/sqrt(1 + x^2)`

• `x/sqrt(1 + x^2)`

Answer 1

`1/sqrt(1 + x^2)`

Explanation:

Let tan y = x ⇒ sin y

= `x/sqrt(1 + x^2)`

Let tan^–1 x = y

∴ y = `sin^-1(x/sqrt(1 + x^2)) => tan^-1x = sin^-1 (x/sqrt(1 + x^2))`

∴ `sin(tan^-1x) = sin(sin^-1(x/sqrt(1 + x^2))) = x/sqrt(1 + x^2)`