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) $±\frac{3}{5}$
Answer & explanation
Correct answer: option 2
We have,
$tan(sec^{-1}x) = sin \left(cos^{-1}\frac{1}{\sqrt{5}}\right)$
$⇒ \sqrt{sec^2(sec^{-1}x)-1}= sin \left(sin^{-1}\frac{2}{\sqrt{5}}\right)$
$⇒ \sqrt{x^2-1} =\frac{2}{\sqrt{5}} ⇒ x = ± \frac{3}{\sqrt{5}}$