Question

If $\frac{\sec \theta +\cos \theta }{\sec \theta -\cos \theta }=2$ then find the value of $\cos \theta$.

Answer 1

Given,

$\frac{\sec \theta +\cos \theta }{\sec \theta -\cos \theta }=2$

or, $\sec \theta +\cos \theta =2\sec \theta -2\cos \theta$

or, $3\cos \theta =\sec \theta$

or, ${\cos }^2\theta =\frac{1}{3}$

or, $\cos \theta =\pm \frac{1}{\sqrt{3}}$