Question

If $\sec \theta =x+\frac{1}{4x}$, prove that :
$\sec \theta +\tan \theta =2x$

Answer 1

$\sec \theta =x+\frac{1}{4x}$

$\tan \theta =\sqrt{{\sec }^2\theta -1}=\sqrt{x^2+\frac{1}{16x^2}+\frac{1}{2}-1}=x-\frac{1}{4x}.$

$\therefore \sec \theta +\tan \theta =2x.$ $\left(proved\right)$