If (tan θ + cot θ) = 5 then (tan2 θ + cot2 θ) = ?

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

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

Squaring both sides, we get

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

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

$\Rightarrow \tan ^{2} \theta+\cot ^{2} \theta+2\left(\frac{1}{\tan \theta}\right)(\tan \theta)=25 \quad\left(\because \cot \theta=\frac{1}{\tan \theta}\right)$

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

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

Hence, the correct option is (d).