Question

$\tan \left({\cos }^{-1}x\right)$, where $\left|x\right|\le 1$ is equal to-

• A. $\frac{\sqrt{1-x^2}}{x}$
• B. $\frac{x}{\sqrt{1+x^2}}$
• C. $\frac{\sqrt{1+x^2}}{x}$
• D. $\frac{x}{\sqrt{1-x^2}}$

Answer 1

The correct option is A $\frac{\sqrt{1-x^2}}{x}$

The value of $\tan \left({\cos }^{-1}x\right)$

$=\tan \left({\tan }^{-1}\left(\frac{\sqrt{1-x^2}}{x}\right)\right)$

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