Question

Solve: ${\tan }^2\theta +{\cot }^2\theta =2$

Answer 1

${\tan }^2\theta +{\cot }^2\theta -2=0$

$\Rightarrow {\tan }^2\theta +{\cot }^2\theta -2\tan \theta \cot \theta =0$

$\Rightarrow {(\tan \theta -\cot \theta )}^2=0$

$\Rightarrow \tan \theta -\cot \theta =0$

$\Rightarrow \tan \theta =\cot \theta$

$\Rightarrow \tan \theta =\frac{1}{\tan \theta }$

$\Rightarrow {\tan }^2\theta =1$

$\therefore \theta =n\pi \pm \frac{\pi }{4}$