Question

If $\tan \theta +\frac{1}{\tan \theta }=2$, find the value of ${\tan }^2\theta +\frac{1}{{\tan }^2\theta }$.

Answer 1

We have,

$\tan \theta +\frac{1}{\tan \theta }=2$

$(\tan \theta +\frac{1}{\tan \theta }{)}^2=4$

${\tan }^2\theta +\frac{1}{{\tan }^2\theta }+2=4$

${\tan }^2\theta +\frac{1}{{\tan }^2\theta }=2$