Question

The value of $tan\left(si{n}^{-1}\right(cos\left(si{n}^{-1}x\right)\left)\right)tan\left(co{s}^{-1}\right(sin\left(co{s}^{-1}x\right)\left)\right)$, where $xϵ(0,1)$, is equal to

• A. $0$
• B. $1$
• C. $-1$
• D. $noneofthese$

Answer 1

The correct option is B $1$

$cossi{n}^{-1}x=\sqrt{1-x^2}$
$tansi{n}^{-1}\left(\sqrt{1-x^2}\right)=\frac{\sqrt{1-x^2}}{x}$
$sin\left(co{s}^{-1}x\right)=\sqrt{1-x^2})$
$tanco{s}^{-1}\left(\sqrt{1-x^2}\right)=\frac{x}{\sqrt{1-x^2}}$
Hence, option B is correct.