Question

$\cos ({\tan }^{-1}x)=?$

• A. $\sqrt{1+x^2}$
• B. $\frac{1}{\sqrt{1+x^2}}$
• C. $1+x^2$
• D. None of these

Answer 1

The correct option is B

$\frac{1}{\sqrt{1+x^2}}$

Explanation for the correct option:

Let $\theta ={\tan }^{-1}x$

$\Rightarrow$$x=\tan \theta$

$\because$$\cos \theta =\frac{1}{\left[\sqrt{1+{\tan }^2\theta }\right]}$

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

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

Hence, Option ‘B’ is Correct.