If (tan θ + cot θ) = 5, find the value of (tan²θ + cot²θ).

As, (tan θ + cot θ) = 5

Squaring both sides, we get :

⇒ (tan θ + cot θ)² = 5²

⇒ tan²θ + cot²θ + 2 tan θ cot θ = 25

⇒ tan²θ + cot²θ + $2\tan \theta \times \dfrac{1}{\tan \theta}$ = 25

⇒ tan²θ + cot²θ + 2 = 25

⇒ tan²θ + cot²θ = 25 - 2

⇒ tan²θ + cot²θ = 23.

Hence, tan²θ + cot²θ = 23.