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  1. If θ be acute and tan θ + cot θ = 2, then the value of tan5 θ + cot10 θ is
    1. 1
    2. 2
    3. 3
    4. 4
Correct Option: B

tan θ + cot θ = 2

⇒tan θ +
1
= 2
tan θ

⇒ tan² θ + 1 = 2tan θ
⇒ tan² θ – 2tan θ + 1 = 0
⇒ (tan θ – 1)² = 0
⇒ tan θ = 1 ⇒ cot θ = 1
∴ tan5 θ + cot10 θ = 1 + 1 = 2


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