The value of cot ( sin - 1 x ) is:

Question

The value of $\cot (\sin^{- 1} x)$ is:

Smart Achievers · Accepted Answer

(4)

Ans. $\frac{\sqrt{1 - x^{2}}}{x}$

Explanation:

Let $\sin^{- 1} x = θ$ ,

then $\sin θ = x$

$\Rightarrow$ $c o s e c θ = \frac{1}{x}$

$\Rightarrow$ $c o s e c^{2} θ = \frac{1}{x^{2}}$

$\Rightarrow$ $1 + \cot^{2} θ = \frac{1}{x^{2}}$

$\Rightarrow$ $\cot θ = \frac{\sqrt{1 - x^{2}}}{x}$

$\Rightarrow$ $\cot (\sin^{- 1} x) = \frac{\sqrt{1 - x^{2}}}{x}$

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