If tan θ + cot θ = 2, then the value of tan100θ

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If tan θ + cot θ = 2, then the value of tan¹⁰⁰θ + cot¹⁰⁰θ is

1. 2
2. 0
3. 1
4. √3

Correct Option: A

tan θ + cot θ = 2

⇒ tan θ +	1	= 2
	tan θ

⇒ tan²θ + 1 = 2 tanθ
⇒ tan²θ – 2tan θ + 1 = 0
⇒ (tanθ – 1)² = 0
⇒ tan θ = 1

∴ cot θ =	1	= 1
	tan θ

∴ tan¹⁰⁰ θ + cot¹⁰⁰ θ = 1 + 1 = 2