If tan Theta cot Theta 5 then tan2 Theta cot2 Theta is ........

Quantitative Aptitude ( CCS) Trignometry

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If tan Θ + cot Θ = 5, then tan²Θ + cot²Θ is:

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Explanation:

From the given equation,
tanΘ + cotΘ = 5
Now, squaring both sides, we get
⇒ (tanΘ + cotΘ)² = (5)²
⇒ tan²Θ + cot²Θ + 2 tanΘ cotΘ = 25
⇒ tan²Θ + cot²Θ + 2 tanΘ /tanΘ = 25
... By applying cotΘ = 1 /tanΘ
⇒ tan²Θ + cot²Θ + 2 = 25
⇒ tan²Θ + cot²Θ = 25 – 2
⇒ tan²Θ + cot²Θ = 23.