Question

Value it:-
It $\tan \theta +\cot \theta =2$, find the value of ${\tan }^2\theta +{\cot }^2\theta$.

Answer 1

$tan\theta +cot\theta =2$

Squaring both sides,

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

$ta{n}^2\theta +co{t}^2\theta +2tan\theta cot\theta =4$

$ta{n}^2\theta +co{t}^2\theta =4-2\times tan\theta \times \frac{1}{tan\theta }$

$[\because cot\theta =\frac{1}{tan\theta }]$

$\Rightarrow ta{n}^2\theta +co{t}^2\theta =2$