Question

If $\tan$ $\theta$ + $\cot$ $\theta$ = 2, find the value of ${\tan }^2\theta +{\cot }^2\theta$

Answer 1

$\tan \theta +\cot \theta =2$

Squaring both sides;

$(\tan \theta +\cot \theta {)}^2=2^2$

$\Rightarrow {\tan }^2\theta +{\cot }^2\theta +2\tan \theta \cot \theta =4$

$\Rightarrow {\tan }^2\theta +{\cot }^2\theta +2=4$

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