If θ is an acute angle and tan θ + cot θ

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If θ is an acute angle and tan θ + cot θ = 2, then the value of tan⁵ θ + cot⁵ θ is

tan θ + cot θ = 2

⇒ tan θ +	1	= 2
	tan θ

⇒	tan² θ + 1	= 2
	tan θ

⇒ tan² θ +1 = 2 tanθ
⇒ tan²θ – 2 tan θ + 1 = 0
⇒ (tan θ –1)² = 0
⇒ tanθ – 1= 0 ⇒ tanθ = 1

∴ cot θ =	1	= 1
	tan θ

∴ tan⁵θ + cot⁵θ = 1 + 1 = 2