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


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 $tan\theta .cot\theta =1$]

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

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


Updated on: 10-Oct-2022

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