The value of the trigonometric function tan (cot-1x) is equal to?

# The value of the trigonometric function tan (${\mathit{cot}}^{-1}x$) is equal to?

1. A
$\frac{1}{x}$
2. B
cot (${\mathit{tan}}^{-1}x$)
3. C
Both
4. D
None

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### Solution:

We know that (${\mathit{cot}}^{-1}x$) = ${\mathit{tan}}^{-1}\frac{1}{x}$; x > 0
Given, tan (${\mathit{cot}}^{-1}x$)
$⇒$ tan (${\mathit{tan}}^{-1}\frac{1}{x}$)
Now using the property tan (${\mathit{tan}}^{-1}x$) = x, x $\in$ R we get,
$⇒$ $\frac{1}{x}$ .
Also, tan (${\mathit{cot}}^{-1}x$)
$⇒$ tan
By using Cot $\Theta$ = tan we get
$⇒$cot ${\left(\mathit{tan}}^{-1}x\right)$.

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