Q. What is $\tan (\cos^{-1} \, x) $ equal to ?
Inverse Trigonometric Functions
Solution:
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} $
