Question

Solve for $x$, if
$\tan \left({\cos }^{-1}x\right)=\frac{2}{\sqrt{5}}$

Answer 1

Given, $\tan \left({\cos }^{-1}x\right)=\frac{2}{\sqrt{5}}$
Let ${\cos }^{-1}x=\theta$
$\Rightarrow x=\cos \theta$
$\Rightarrow \tan \theta =\frac{2}{\sqrt{5}}$
which gives $\cos \theta =\frac{\sqrt{5}}{3}$
Hence $x=\frac{\sqrt{5}}{3}$