Question

The value of cot (sin^–1x) is ______.

विकल्प

• `sqrt(1 + x^2)/x`

• `x/sqrt(1 + x^2)`

• `1/x`

• `sqrt(1 - x^2)/x`

Answer 1

The value of cot (sin^–1x) is `sqrt(1 - x^2)/x`.

Explanation:

Let sin^–1x = θ, then sin θ = x

⇒ cosec θ = `1/x`

⇒ cosec²θ = `1/x^2`

⇒ 1 + cot²θ = `1/x^2`

⇒ cot θ = `sqrt(1 - x^2)/x`.