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

Given: $tan\theta +cot\theta =5$.

To do: To find the value of $tan^{2} \theta +cot^{2} \theta $.

Solution: As given, $tan\theta +cot\theta =5$

On squaring both sides,

$( tan\theta +cot\theta )^{2} =5^{2}$

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

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

$\Rightarrow tan^{2} \theta +cot^{2} \theta =25-2$

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

Tutorialspoint

Updated on: 10-Oct-2022

81 Views

Kickstart Your Career

Get certified by completing the course

Get Started