The values of x satisfying $tan(sec^{-1}x) = sin \left(cos^{-1}\frac{1}{\sqrt{5}}\right)$, is

(a) $±\frac{\sqrt{5}}{3}$

(b) $±\frac{3}{\sqrt{5}}$

(c) $±\frac{\sqrt{3}}{5}$

(d) $±\frac{3}{5}$

(b)

We have, 

$tan(sec^{-1}x) = sin \left(cos^{-1}\frac{1}{\sqrt{5}}\right)$

$⇒ \sqrt{sec^2(sec^{-1}x)-1}= sin \left(sin^{-1}\frac{2}{\sqrt{5}}\right)$

$⇒ \sqrt{x^2-1} =\frac{2}{\sqrt{5}} ⇒ x = ± \frac{3}{\sqrt{5}}$