If tan θ + cot θ = 5, then tan²θ

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tanθ + cotθ = 5
On squaring both sides, (tanθ + cotθ)² = 52
⇒ tan² θ + cot² θ + 2 tanθ.cotθ = 25
⇒ tan² θ + cot² θ = 25 – 2 = 23 [∵ tanθ.cotθ = 1]