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

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If tan θ + cot θ = 2, then the value of tanⁿ θ + cotⁿθ (0° < θ < 90°, n is an integer) is

tan θ + cot θ = 2

⇒ tan θ +	1	= 2
	tan θ

⇒ tan⊃ θ - 2tan θ + 1 = 0
⇒ (tan θ - 1)² = 0
⇒ tanθ = 1 0 ⇒ tanθ = 1
∴ cot θ = ⇒ θ= 45°
∴ tanⁿ 45° + cotⁿ 45° = 1 + 1 = 2