Question

${\tan }^2\theta +{\cot }^2\theta =2$. Then $\theta =$

Answer 1

${\tan }^2\theta +\left(1/{\tan }^2\theta \right)-2=0$
or ${\tan }^4\theta -2{\tan }^2\theta +1=0$
$\therefore ({\tan }^2\theta -1{)}^2=0$
$\therefore {\tan }^2\theta =1$
or $\tan \theta =\pm 1=\pm \tan \left(\pi /4\right)$
$\therefore \theta =n\pi \pm \pi /4$.