Question

Find the value of ${\tan }^2\theta +\frac{1}{{\tan }^2\theta }$ if $\tan \theta +\frac{1}{\tan \theta }=2$

Answer 1

Given,

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

Squaring both sides we get

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

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

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

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