Question

If ${\sec }^2\theta =2+2\tan \theta$, find $\tan \theta$.

Answer 1

Given ${\text{sec}}^2\theta =2+2\tan \theta$

$⟹1+{\tan }^2\theta =2+2\tan \theta$

$⟹{\tan }^2\theta -2\tan \theta -1=0$

$⟹\tan \theta =\frac{2\pm \sqrt{4+4}}{2}=1\pm \sqrt{2}$