Question

1. The value of cot(sin-1 x) is:​

Answer 1

1. The value of cot(sin-1 x) is:​

Given,

$cot (sin^{-1}x)$

Let,

$x = sin \theta\\\\\Rightarrow cos \theta = \sqrt {1-x^2}\\\\\because sin^2 \theta + cos^2 \theta =1$

Now, we have,

$cot (sin^{-1}x)$

$cot (sin^{-1}sin \theta)\\\\= cot \theta\\\\= \dfrac{cos \theta} {sin \theta}$

$=\dfrac{\sqrt {1-x^2}}{x}$

Therefore, option A is correct.