Question

What is $\tan ({\cos }^{-1}x)$ equal to ?

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

Answer 1

Answer: (A)

Let ${\cos }^{-1}x=\theta$
$\Rightarrow \cos \theta =x\Rightarrow \sin \theta =\sqrt{1-x^2}$
$\Rightarrow \tan \theta =\frac{\sqrt{1-x^2}}{x}$ and $\theta ={\cos }^{-1}x$
This can be represented by a triangle with hypotenuse = 1 and sides x and $\sqrt{1-x^2}$ .
$\Rightarrow \tan \left({\cos }^{-1}x\right)=\frac{\sqrt{1-x^2}}{x}$