Question

If $\tan \theta +\cot \theta =5,$ find the value of ${\tan }^2\theta +{\cot }^2\theta$.

Answer 1

Given,

$\tan \theta +\cot \theta =5$

Now squaring both sides we get,

$\Rightarrow ({\tan }^2\theta +{\cot }^2\theta +2.\tan \theta .\cot \theta )=25$

$\Rightarrow {\tan }^2\theta +{\cot }^2\theta =25-2$ [ Since $\tan \theta .\cot \theta =1$]

$\Rightarrow {\tan }^2\theta +{\cot }^2\theta =23$.